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Only after passage of the federal Civil Rights Act of 1964 and Voting Rights Act of 1965 did African Americans regain the ability to exercise suffrage, among other civil rights. In many jurisdictions, they continued to be excluded from representation by at-large electoral systems, which allowed the majority of the population to dominate elections. Some changes at the county level have occurred following court challenges to establish single-member districts that enable a more diverse representation among county boards.
In 2007, the Alabama Legislature passed, and Republican governor Bob Riley signed a resolution expressing "profound regret" over slavery and its lingering impact. In a symbolic
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ceremony, the bill was signed in the Alabama State Capitol, which housed Congress of the Confederate States of America.
In 2010, Republicans won control of both houses of the legislature for the first time in 136 years.
, there are a total of 3,326,812 registered voters, with 2,979,576 active, and the others inactive in the state.
## Elections.
### State elections.
With the disfranchisement of Blacks in 1901, the state became part of the "Solid South", a system in which the Democratic Party operated as effectively the only viable political party in every Southern state. For nearly 100 years, local and state elections in Alabama were decided in the Democratic Party primary, with generally
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only token Republican challengers running in the General Election. Since the mid to late 20th century, however, there has been a realignment among the two major political parties, and white conservatives started shifting to the Republican Party. In Alabama, majority-white districts are now expected to regularly elect Republican candidates to federal, state and local office.
Members of the nine seats on the Supreme Court of Alabama and all ten seats on the state appellate courts are elected to office. Until 1994, no Republicans held any of the court seats. In that general election, the then-incumbent chief justice, Ernest C. Hornsby, refused to leave office after losing the election by approximately
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3,000 votes to Republican Perry O. Hooper, Sr.. Hornsby sued Alabama and defiantly remained in office for nearly a year before finally giving up the seat after losing in court. This ultimately led to a collapse of support for Democrats at the ballot box in the next three or four election cycles. The Democrats lost the last of the nineteen court seats in August 2011 with the resignation of the last Democrat on the bench.
In the early 21st century, Republicans hold all seven of the statewide elected executive branch offices. Republicans hold six of the eight elected seats on the Alabama State Board of Education. In 2010, Republicans took large majorities of both chambers of the state legislature,
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giving them control of that body for the first time in 136 years. The last remaining statewide Democrat, who served on the Alabama Public Service Commission was defeated in 2012.
Only three Republican lieutenant governors have been elected since the end of Reconstruction, when Republicans generally represented Reconstruction government, including the newly emancipated freedmen who had gained the franchise. The three GOP lieutenant governors are Steve Windom (1999–2003), Kay Ivey (2011–2017), and Will Ainsworth (2019–present).
### Local elections.
Many local offices (county commissioners, boards of education, tax assessors, tax collectors, etc.) in the state are still held by Democrats. Many
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rural counties have voters who are majority Democrats, resulting in local elections being decided in the Democratic primary. Similarly many metropolitan and suburban counties are majority-Republican and elections are effectively decided in the Republican Primary, although there are exceptions.
Alabama's 67 county sheriffs are elected in partisan, at-large races, and Democrats still retain the narrow majority of those posts. The current split is 35 Democrats, 31 Republicans, and one Independent Fayette. However, most of the Democratic sheriffs preside over rural and less populated counties. The majority of Republican sheriffs have been elected in the more urban/suburban and heavily populated
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counties. , the state of Alabama has one female sheriff, in Morgan County, Alabama, and ten African-American sheriffs.
### Federal elections.
The state's two U.S. senators are Republican Richard C. Shelby and Democrat Doug Jones. Shelby was originally elected to the Senate as a Democrat in 1986 and re-elected in 1992, but switched parties immediately following the November 1994 general election.
In the U.S. House of Representatives, the state is represented by seven members, six of whom are Republicans: (Bradley Byrne, Mike D. Rogers, Robert Aderholt, Morris J. Brooks, Martha Roby, and Gary Palmer) and one Democrat: Terri Sewell who represents the Black Belt as well as most of the predominantly
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black portions of Birmingham, Tuscaloosa and Montgomery.
# Education.
## Primary and secondary education.
Public primary and secondary education in Alabama is under the purview of the Alabama State Board of Education as well as local oversight by 67 county school boards and 60 city boards of education. Together, 1,496 individual schools provide education for 744,637 elementary and secondary students.
Public school funding is appropriated through the Alabama Legislature through the Education Trust Fund. In FY 2006–2007, Alabama appropriated $3,775,163,578 for primary and secondary education. That represented an increase of $444,736,387 over the previous fiscal year. In 2007, over 82 percent
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of schools made adequate yearly progress (AYP) toward student proficiency under the National No Child Left Behind law, using measures determined by the state of Alabama.
While Alabama's public education system has improved in recent decades, it lags behind in achievement compared to other states. According to U.S. Census data (2000), Alabama's high school graduation rate (75%) is the fourth lowest in the U.S. (after Kentucky, Louisiana and Mississippi). The largest educational gains were among people with some college education but without degrees.
Although unusual in the West, school corporal punishment is not uncommon in Alabama, with 27,260 public school students paddled at least one time,
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according to government data for the 2011–2012 school year. The rate of school corporal punishment in Alabama is surpassed only by Mississippi and Arkansas.
## Colleges and universities.
Alabama's programs of higher education include 14 four-year public universities, two-year community colleges, and 17 private, undergraduate and graduate universities. In the state are four medical schools (as of fall 2015) (University of Alabama School of Medicine, University of South Alabama and Alabama College of Osteopathic Medicine and The Edward Via College of Osteopathic Medicine – Auburn Campus), two veterinary colleges (Auburn University and Tuskegee University), a dental school (University of Alabama
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School of Dentistry), an optometry college (University of Alabama at Birmingham), two pharmacy schools (Auburn University and Samford University), and five law schools (University of Alabama School of Law, Birmingham School of Law, Cumberland School of Law, Miles Law School, and the Thomas Goode Jones School of Law). Public, post-secondary education in Alabama is overseen by the Alabama Commission on Higher Education and the Alabama Department of Postsecondary Education. Colleges and universities in Alabama offer degree programs from two-year associate degrees to a multitude of doctoral level programs.
The largest single campus is the University of Alabama, located in Tuscaloosa, with 37,665
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enrolled for fall 2016. Troy University was the largest institution in the state in 2010, with an enrollment of 29,689 students across four Alabama campuses (Troy, Dothan, Montgomery, and Phenix City), as well as sixty learning sites in seventeen other states and eleven other countries. The oldest institutions are the public University of North Alabama in Florence and the Catholic Church-affiliated Spring Hill College in Mobile, both founded in 1830.
Accreditation of academic programs is through the Southern Association of Colleges and Schools (SACS) as well as other subject-focused national and international accreditation agencies such as the Association for Biblical Higher Education (ABHE),
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the Council on Occupational Education (COE), and the Accrediting Council for Independent Colleges and Schools (ACICS).
According to the 2011 "U.S. News & World Report", Alabama had three universities ranked in the top 100 Public Schools in America (University of Alabama at 31, Auburn University at 36, and University of Alabama at Birmingham at 73).
According to the 2012 "U.S. News & World Report", Alabama had four tier 1 universities (University of Alabama, Auburn University, University of Alabama at Birmingham and University of Alabama in Huntsville).
# Media.
Major newspapers include "Birmingham News", Mobile "Press-Register", and "Montgomery Advertiser".
Major television network affiliates
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in Alabama include:
- ABC
- WGWW 40.2 ABC, Anniston
- WBMA 58/WABM 68.2 ABC, Birmingham
- WDHN 18 ABC, Dothan
- WAAY 31 ABC, Huntsville
- WEAR 3 ABC Pensacola, FL/Mobile
- WNCF 32 ABC, Montgomery
- WDBB 17.2 ABC, Tuscaloosa
- CBS
- WIAT 42 CBS, Birmingham
- WTVY 4 CBS, Dothan
- WHNT 19 CBS, Huntsville
- WKRG 5 CBS, Mobile
- WAKA 8 CBS, Selma/Montgomery
- Fox
- WBRC 6 FOX, Birmingham
- WZDX 54 FOX, Huntsville
- WALA 10 FOX, Mobile
- WCOV 20 FOX, Montgomery
- WDFX 34 FOX, Ozark/Dothan
- NBC
- WVTM 13 NBC, Birmingham
- WRGX 23 NBC, Dothan
- WAFF 48 NBC, Huntsville
- WPMI 15 NBC, Mobile
- WSFA 12 NBC, Montgomery
- PBS/Alabama Public Television
- WBIQ 10 PBS, Birmingham
-
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WIIQ 41 PBS, Demopolis
- WDIQ 2 PBS, Dozier
- WFIQ 36 PBS, Florence
- WHIQ 25 PBS, Huntsville
- WGIQ 43 PBS, Louisville
- WEIQ 42 PBS, Mobile
- WAIQ 26 PBS, Montgomery
- WCIQ 7 PBS, Mount Cheaha
- The CW
- WTTO 21, Homewood/Birmingham
- WTVY 4.3, Dothan
- WHDF 15, Florence/Huntsville
- WFNA 55, Gulf Shores/Mobile/Pensacola, FL
- WDBB 17, Tuscaloosa
- WBMM 22, Tuskegee/Montgomery
# Culture.
## Sports.
### College sports.
College football is extremely popular in Alabama, particularly the University of Alabama Crimson Tide and Auburn University Tigers, rivals in the Southeastern Conference. In the 2013 season, Alabama averaged over 100,000 fans per game and Auburn averaged over
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80,000 fans, both numbers among the top 20 in the nation in average attendance. Bryant–Denny Stadium is the home of the Alabama football team, and has a seating capacity of 101,821, and is the fifth largest stadium in America. Jordan-Hare Stadium is the home field of the Auburn football team and seats up to 87,451.
Legion Field is home for the UAB Blazers football program and the Birmingham Bowl. It seats 71,594. Ladd–Peebles Stadium in Mobile is the home of the University of South Alabama football team, and serves as the home of the NCAA Senior Bowl, Dollar General Bowl (formerly GoDaddy.com Bowl), and Alabama-Mississippi All Star Classic; the stadium seats 40,646. In 2009, Bryant–Denny Stadium
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and Jordan-Hare Stadium became the homes of the Alabama High School Athletic Association state football championship games, after previously being held at Legion Field in Birmingham.
### Professional sports.
Alabama has several professional and semi-professional sports teams, including three minor league baseball teams.
- Notes
The Talladega Superspeedway motorsports complex hosts a series of NASCAR events. It has a seating capacity of 143,000 and is the thirteenth largest stadium in the world and sixth largest stadium in America. Also, the Barber Motorsports Park has hosted IndyCar Series and Rolex Sports Car Series races.
The ATP Birmingham was a World Championship Tennis tournament held
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from 1973 to 1980.
Alabama has hosted several professional golf tournaments, such as the 1984 and 1990 PGA Championship at Shoal Creek, the Barbasol Championship (PGA Tour), the Mobile LPGA Tournament of Champions, Airbus LPGA Classic, and Yokohama Tire LPGA Classic (LPGA Tour), and The Tradition (Champions Tour).
# Transportation.
## Aviation.
Major airports with sustained commercial operations in Alabama include Birmingham-Shuttlesworth International Airport (BHM), Huntsville International Airport (HSV), Dothan Regional Airport (DHN), Mobile Regional Airport (MOB), Montgomery Regional Airport (MGM), and Muscle Shoals – Northwest Alabama Regional Airport (MSL).
## Rail.
For rail transport,
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Amtrak schedules the "Crescent", a daily passenger train, running from New York to New Orleans with station stops at Anniston, Birmingham, and Tuscaloosa.
## Roads.
Alabama has six major interstate roads that cross the state: Interstate 65 (I-65) travels north–south roughly through the middle of the state; I-20/I-59 travel from the central west Mississippi state line to Birmingham, where I-59 continues to the north-east corner of the state and I-20 continues east towards Atlanta; I-85 originates in Montgomery and travels east-northeast to the Georgia state line, providing a main thoroughfare to Atlanta; and I-10 traverses the southernmost portion of the state, traveling from west to east through
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Mobile. I-22 enters the state from Mississippi and connects Birmingham with Memphis, Tennessee. In addition, there are currently five auxiliary interstate routes in the state: I-165 in Mobile, I-359 in Tuscaloosa, I-459 around Birmingham, I-565 in Decatur and Huntsville, and I-759 in Gadsden. A sixth route, I-685, will be formed when I-85 is rerouted along a new southern bypass of Montgomery. A proposed northern bypass of Birmingham will be designated as I-422. Since a direct connection from I-22 to I-422 will not be possible, I-222 has been proposed, as well.
Several U.S. Highways also pass through the state, such as U.S. Route 11 (US-11), US-29, US-31, US-43, US-45, US-72, US-78, US-80, US-82,
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US-84, US-90, US-98, US-231, US-278, US-280, US-331, US-411, and US-431.
There are four toll roads in the state: Montgomery Expressway in Montgomery; Tuscaloosa Bypass in Tuscaloosa; Emerald Mountain Expressway in Wetumpka; and Beach Express in Orange Beach.
## Ports.
The Port of Mobile, Alabama's only saltwater port, is a large seaport on the Gulf of Mexico with inland waterway access to the Midwest by way of the Tennessee-Tombigbee Waterway. The Port of Mobile was ranked 12th by tons of traffic in the United States during 2009. The newly expanded container terminal at the Port of Mobile was ranked as the 25th busiest for container traffic in the nation during 2011. The state's other ports
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are on rivers with access to the Gulf of Mexico.
Water ports of Alabama, listed from north to south:
# See also.
- Outline of Alabama – organized list of topics about Alabama
- Index of Alabama-related articles
- Sweet Home Alabama: a Lynyrd Skynyrd song about the state
# References.
- "Alabama – History and Culture." Adventure Tourism – Experiential Travel Guides. Accessed: March 31, 2017.
# Further reading.
- Atkins, Leah Rawls, Wayne Flynt, William Warren Rogers, and David Ward. "Alabama: The History of a Deep South State" (1994)
- Flynt, Wayne. "Alabama in the Twentieth Century" (2004)
- Owen Thomas M. "History of Alabama and Dictionary of Alabama Biography" 4 vols. 1921.
- Jackson,
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Harvey H. "Inside Alabama: A Personal History of My State" (2004)
- Mohl, Raymond A. "Latinization in the Heart of Dixie: Hispanics in Late-twentieth-century Alabama" "Alabama Review" 2002 55(4): 243–274.
- Peirce, Neal R. "The Deep South States of America: People, Politics, and Power in the Seven Deep South States" (1974). Information on politics and economics 1960–72.
- Williams, Benjamin Buford. "A Literary History of Alabama: The Nineteenth Century" 1979.
- WPA. "Guide to Alabama" (1939)
# External links.
- Alabama State Guide, from the Library of Congress
- All About Alabama, at the Alabama Department of Archives and History
- Code of Alabama 1975 – at the Alabama Legislature site
-
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4): 243–274.
- Peirce, Neal R. "The Deep South States of America: People, Politics, and Power in the Seven Deep South States" (1974). Information on politics and economics 1960–72.
- Williams, Benjamin Buford. "A Literary History of Alabama: The Nineteenth Century" 1979.
- WPA. "Guide to Alabama" (1939)
# External links.
- Alabama State Guide, from the Library of Congress
- All About Alabama, at the Alabama Department of Archives and History
- Code of Alabama 1975 – at the Alabama Legislature site
- USGS real-time, geographic, and other scientific resources of Alabama
- Alabama QuickFacts from the U.S. Census Bureau
- Alabama State Fact Sheet from the U.S. Department of Agriculture
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Battle of Montereau
The Battle of Montereau (18 February 1814) was fought during the War of the Sixth Coalition between an Imperial French army led by Emperor Napoleon and a corps of Austrians and Württembergers commanded by Crown Prince Frederick William of Württemberg. While Napoleon's army mauled an Allied army under Gebhard Leberecht von Blücher, the main Allied army commanded by Karl Philipp, Prince of Schwarzenberg advanced to a position dangerously close to Paris. Gathering up his outnumbered forces, Napoleon rushed his soldiers south to deal with Schwarzenberg. Hearing of the approach of the French emperor, the Allied commander ordered a withdrawal, but 17 February saw his rear guards
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overrun or brushed aside.
Ordered to hold Montereau until nightfall on the 18th, the Crown Prince of Württemberg posted a strong force on the north bank of the Seine River. All morning and past noon, the Allies stoutly held off a series of French attacks. However, under increasing French pressure, the Crown Prince's lines buckled in the afternoon and his troops ran for the single bridge to their rear. Brilliantly led by Pierre Claude Pajol, the French cavalry got among the fugitives, captured the spans over both the Seine and Yonne Rivers and seized Montereau. The Allied force suffered heavy losses and the defeat confirmed Schwarzenberg's decision to continue the retreat to Troyes.
# Background.
##
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Allied advance.
On 10 February, the Army of Bohemia under Karl Philipp, Prince of Schwarzenberg began advancing from Troyes. On the right, Peter Wittgenstein and Karl Philipp von Wrede headed for Nogent and Bray on the Seine River supported by the Guards and Reserves. On the left, Crown Prince Frederick William of Württemberg moved on Sens with the I Corps of Frederick Bianchi, Duke of Casalanza on his left. The left flank forces were backed by Ignaz Gyulai's corps. The Allies were briefly checked at Nogent on the 10th by 1,000 French troops under Louis-Auguste-Victor, Count de Ghaisnes de Bourmont. Sens was taken on the 11th after a skirmish between the Crown Prince and Jacques-Alexandre-François
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Allix de Vaux.
Tasked with the defense of the Seine, Marshal Claude Perrin Victor held Nogent and Marshal Nicolas Oudinot defended Montereau. On the 12th the Allies captured Bray from a weak force of French National Guards as well as the bridge at Pont-sur-Seine near Montereau. Afraid of being surrounded, Victor evacuated Nogent and fell back. The appearance of troops under Marshal Jacques MacDonald did not stop the retreat and by 15 February the French were moving back to the Yerres River only from Paris. Alexander Nikitich Seslavin led a scouting force of three Russian hussar squadrons and one Cossack regiment well to the south to seize Montargis and threaten Orléans. Auxerre was stormed
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and its garrison wiped out. Cossacks roamed freely in the Forest and Palace of Fontainebleau. When Victor's wagon train appeared at Charenton-le-Pont the Parisians were thrown into panic. Meanwhile, fleeing peasants reported that Paris would soon be attacked by 200,000 Cossacks.
## French counteroffensive.
Following his successes in the Six Days' Campaign on 10–14 February 1814, Emperor Napoleon headed southward towards the Seine to stop Schwarzenberg's threat to Paris. Forces under Marshals Édouard Mortier and Auguste Marmont were left behind to keep Gebhard Leberecht von Blücher's Army of Silesia under observation. Giving up his plans to finish off Blücher, Napoleon left Montmirail on 15
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February with the Imperial Guard and Emmanuel Grouchy's cavalry. In an epic march, with some infantry traveling in carts and wagons, Napoleon's leading forces reached Guignes at 3:00 pm on the 16th after moving in 36 hours. Another authority stated that some troops marched in 36 hours.
Hearing of Blücher's defeat and the approach of Napoleon, the cautious Schwarzenberg scrambled to put the Seine between his army and the French emperor. On 17 February, he ordered Wittgenstein to retreat to Provins while Michael Andreas Barclay de Tolly massed the Russian and Prussian Guards near Nogent. He instructed Wrede to fall back to Donnemarie while leaving an advanced guard at Nangis. Württemberg and
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Bianchi were posted near Montereau while Gyulai held Pont-sur-Yonne and the Austrian Reserve was at Sens. If the Army of Bohemia needed to retreat farther, it was important to hold the position at Montereau. Matvei Platov was to the west at Nemours where his 2,100 Cossacks captured 600 men of an Imperial Guard depot battalion on the 16th.
Early on 17 February, Napoleon's leading elements under Etienne Maurice Gérard enveloped a Russian force led by Peter Petrovich Pahlen. In the Battle of Mormant, Pahlen's 2,500 infantry and 1,250 cavalry were overwhelmed by the French, suffering 3,114 killed, wounded or captured. A nearby Austrian force led by Anton von Hardegg remained largely inert while
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its allies were being cut to pieces. Finally, Hardegg allowed 550 troopers from the Schwarzenberg Uhlan Regiment Nr. 2 to assist the Russians. The Reval and Selenginsk Infantry Regiments suffered such heavy losses that they were withdrawn from the campaign. Next, the French struck Wrede's advance guard at Nangis and threw it back to Villeneuve-le-Comte.
At Nangis Napoleon split his army into three columns. The right column including Victor's II Corps, Gerard's Reserve of Paris and cavalry under Samuel-François Lhéritier and Étienne Tardif de Pommeroux de Bordesoulle took the road south toward Montereau. The center column consisted of MacDonald's XI Corps, two cavalry divisions and the Imperial
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Guard. This force headed for Bray. The left column, made up of Oudinot's VII Corps and François Étienne de Kellermann's cavalry, pursued Wittgenstein east toward Provins. Pierre Claude Pajol's cavalry and Michel-Marie Pacthod's National Guards set out from Melun and advanced southeast toward Montereau. The divisions of Allix and Henri François Marie Charpentier moved south from Melun to Fontainebleau. MacDonald and Oudinot pressed Hardegg's rear guard back, capturing some wagons. Victor came across one of Wrede's divisions drawn up on the heights of Valjouan near Villeneuve. Victor sent Gérard to attack the Bavarians in front while Bordesoulle circled to take them from behind. Soon the Bavarians
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were retreating in disorder and Lhéritier missed a chance to deliver the "coup de grace" with his cavalry. Nevertheless, Wrede's corps sustained 2,500 casualties during the day. Victor's soldiers were exhausted, so he called a halt. Napoleon was furious that Victor disobeyed his orders to press on to Montereau during the night and asked his chief of staff Louis-Alexandre Berthier to write him a harsh reprimand.
# Battle.
## Forces.
The Crown Prince's IV Corps consisted of an infantry division led by Christian Johann Gottgetreu von Koch and a cavalry division under Prince Adam von Württemberg. Ludwig Stockmeyer's brigade consisted of two battalions of King Frederick Jäger Regiment Nr. 9 and
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one battalion of Light Infantry Regiment Nr. 10. Christoph Friedrich David Döring's brigade was made up of two battalions each of Infantry Regiments Duke Wilhelm Nr. 2, Nr. 3 and Nr. 7. Prince Karl von Hohenlohe-Kirchberg's brigade included two battalions each of Infantry Regiments Nr. 4 and Crown Prince Nr. 6. Walsleben's cavalry brigade comprised four squadrons each of Duke Louis Jäger zu Pferde Regiment Nr. 2 and Crown Prince Dragoon Regiment Nr. 3. Karl August Maximillian Jett's cavalry brigade had four squadrons of Prince Adam Jäger zu Pferde Regiment Nr. 4. Attached to each cavalry brigade was one horse artillery battery while Döring's and Hohenlohe's brigades each had a foot artillery
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battery. All four batteries were armed with four 6-pound cannons and two howitzers.
Attached to the IV Corps was Joseph Schäffer's Austrian brigade. This unit consisted of two battalions each of Infantry Regiments Gyulai Nr. 21, Esterhazy Nr. 32 and Josef Colloredo Nr. 57, three battalions of Infantry Regiment Zach Nr. 15, six squadrons of Archduke Ferdinand Hussar Regiment Nr. 3 and two-foot artillery batteries. Altogether there were 11,000 Württembergers and 4,000 Austrians present. A second source credited the Allies with 18,000 troops in Montereau.
Victor's II Corps had the divisions of Louis Huguet-Chateau and Guillaume Philibert Duhesme. Chateau's 1st Division was made up of 1st Battalions
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of the 11th and 24th Light and the 2nd, 19th, 37th and 56th Line Infantry Regiments. Duhesme's 2nd Division included 1st and 2nd Battalions of the 4th, 18th and 46th Line and 1st Battalions of the 72nd and 93rd Line and 26th Light. Chateau's division numbered only 1,536 officers and men, since all units except the 477-strong 19th were sadly understrength, while Duhesme had 2,442 effectives. The 1st Division was supported by five 6-pound cannons and one howitzer while the 2nd Division counted eight 6-pound cannons and four howitzers. With 475 gunners and 135 sappers, Victor's total strength was 4,588 soldiers. Gérard's Reserve of Paris included the divisions of Georges Joseph Dufour and Jacques
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Félix Jan de La Hamelinaye. The 1st Division was made up of one battalion each of the 5th, 12th, 15th and 29th Light and the 32nd, 58th and 135th Line. The 2nd Division comprised the 26th, 82nd, 86th, 121st, 122nd and 142nd Line. Gérard's force had 214 artillerists from three companies attached.
Pajol led a provisional cavalry corps consisting of three small brigades, 460 Chasseurs à Cheval under Jacques-Antoine-Adrien Delort, 476 Dragoons under François Grouvel and 400 Hussars under Charles Yves César Du Coetlosquet. Pacthod commanded 3,000 National Guards and there were 800 gendarmes (military police) with this column. MacDonald's XI Corps counted three divisions led by Joseph Jean Baptiste
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Albert, François Pierre Joseph Amey and Michel Sylvestre Brayer. Lhéritier commanded the V Cavalry Corps which was formed from three mounted divisions. Hippolyte Piré's 3rd Light Cavalry Division included the 14th, 26th and 27th Chasseurs à Cheval and the 3rd Hussars, André Louis Briche's 3rd Heavy Cavalry Division the 2nd, 6th, 11th, 13th and 15th Dragoons and Lhéritier's 4th Cavalry Division the 18th, 19th, 20th, 22nd and 25th Dragoons. Bordesoulle's detachment numbered 500 horsemen from depot squadrons.
The Imperial Guard consisted of the Old Guard Division of Louis Friant, the 1st Young Guard Division of Claude Marie Meunier, the 2nd Young Guard Division of Philibert Jean-Baptiste Curial,
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and the 2nd and 3rd Guard Cavalry Divisions. Marshal Michel Ney led the two Young Guard divisions while Étienne Marie Antoine Champion de Nansouty led the Guard cavalry divisions. The 2nd Guard Cavalry was made up of the 1st Polish Guard Lancer, Empress Dragoon and Polish and 3rd Éclaireur Regiments. The 3rd Guard Cavalry Division had the Guard Horse Grenadier and Guard Chasseurs à Cheval Regiments. According to one authority, units that fought in the battle included most of the regiments from the corps of Victor and Gérard, the Guard artillery, Guard Chasseurs à Cheval and 2nd Guard Lancers, 3rd Hussars from Jacques Gervais, baron Subervie's brigade, 18th Dragoons of Auguste Lamotte's brigade,
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25th Dragoons from Jean Antoine de Collaert's brigade, 9th Lancers and 22nd Chasseurs à Cheval from Kellermann's VI Cavalry Corps and the 7th Lancers, 9th Chasseurs à Cheval and 7th Hussars from unidentified corps. MacDonald's corps and the Guard infantry were not engaged.
## Action.
After issuing conflicting orders concerning the defense of Montereau, Schwarzenberg finally directed the Crown Prince to hold the town until the evening of 18 February. Meanwhile, Oudinot's leading troops found that Wittgenstein had withdrawn across the Seine at Nogent while Wrede was across at Bray. At both places, the Allies broke the bridges. While Montereau on the south bank is in flat terrain, the north bank
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is crowned by a height with a steep slope next to the river and a gentler slope on the north side. Atop the ridge, Surville chateau overlooks the bridges and town of Montereau, which was surrounded by vineyards and meadows to the south and east. The Paris road approached Montereau from the northwest where there was a forest. The road from Salins came from the northeast and ran alongside the river from Courbeton chateau to the bridge. The hamlet of Les Ormeaux was a short distance east of the Paris road. The roads from the north join at the bridge which crosses the Seine to the eastern suburb, then immediately crosses the Yonne into Montereau. The Seine bridge was the site of the Assassination
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of John the Fearless, Duke of Burgundy in 1419.
The Crown Prince deployed 8,500-foot soldiers, 1,000 horsemen and 26 field guns on the north bank of the Seine. A second authority counted 12,000 defenders. The left flank was anchored in Les Ormeaux, the center incorporated the Surville chateau and park while the right flank included the Courbeton chateau and blocked the road from Salins. Two Austrian batteries from Bianchi's corps were positioned on the south bank, one covering each flank. There was also a IV Corps brigade on the south bank near the eastern suburb at the Motteux Farm. Schäffer's Austrians held the Surville park in the center. The Allies were supported by a total of 40 field
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pieces.
Napoleon ordered Victor to be at Montereau at 6:00 am but the first French forces to arrive were Pajol's cavalry and Pacthod's National Guards at 8:00 am. Aside from numbering no more than 4,500 men, the horsemen had almost no training while the National Guards were ill-equipped and ill-trained. They made no impression on the Crown Prince's defenders. Victor leading elements arrived at 9:00 am and their initial attack was repulsed. When the divisions of Chateau and Duhesme reached the field they were thrown into an attack on Les Ormeaux. This was beaten back and Chateau, who was Victor's son-in-law, was fatally wounded. The Württemberg cavalry charged and drove the French horsemen back
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into the forest. Unable to make any progress by 11:00 am, Victor awaited the coming of Gérard's corps. Angry at the marshal's slowness, Napoleon replaced Victor and placed command of the II Corps in Gérard's hands.
Gérard led his troops up the heights but the Allied artillery was well-served and threw back assault after assault. In the afternoon, the Imperial Guard artillery arrived and 40 more guns were brought into action. At 3:00 pm, Napoleon hurled three attack columns at Les Ormeaux and Surville and another one against the Allied right flank along the Seine. While the Guard remained in reserve, the French artillery unleashed a barrage at Surville chateau. The French finally overran Les
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Ormeaux, causing the Crown Prince to order Schäffer's Austrians to cover the retreat. As the Württembergers began pulling back, Pajol launched a cavalry charge down the Paris highway against the Allied left flank. At this time, French infantry rushed the Surville chateau and made its garrison prisoners. There were now 30,000 French troops on the field supported by 70 or 80 field pieces.
At first the withdrawal was conducted in good order, but the Allied soldiers became more disorganized as they tried to negotiate the steep slope. They fell into complete confusion upon encountering a sunken road. Soon, every Allied soldier was running for the Seine bridge. The Crown Prince tried to rally his
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men and was nearly captured by the French cavalry. The French emperor ordered 60 guns onto the Surville heights where they unlimbered and fired their missiles into the fleeing mob of Allies crowding the bridges. When Napoleon personally sighted one of the cannons, his guardsmen begged him to leave. He refused saying, "Courage my friends, the bullet which is to kill me is not yet cast".
Pajol's horsemen charged into the fleeing mass of soldiers and managed to seize first the Seine bridge and then the Yonne bridge before either could be blown up, though they were rigged for demolition. Duhesme's division rapidly crossed after the cavalry and helped clear Montereau of the Allies. The beaten Allies
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joined Hohenlohe's brigade and began a disorderly retreat toward Le Tombe, a village on the road to Bray. The movement was covered by Jett's cavalry brigade. Napoleon sent Marshal François Joseph Lefebvre and his own cavalry escort in pursuit toward Bray. An eyewitness wrote that Lefebvre foamed at the mouth and struck at Allied soldiers with his saber.
# Results.
According to Digby Smith, the Allies had losses of 1,400 killed and wounded, of which the Württembergers lost 92 killed and 714 wounded; Prince Hohenlohe was killed. The French captured 3,600 men, two cannons and two ammunition wagons. Of these totals, the Austrians had about 2,000 casualties and Schäffer became a French prisoner.
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The French lost 2,000 killed and wounded. A source quoted by Smith gave 4,895 Allied casualties and 15 guns lost. Francis Loraine Petre asserted that the Allies lost nearly 5,000 men and 15 field pieces. David G. Chandler stated that the Allies suffered 6,000 casualties and lost 15 cannons; the French lost 2,500 casualties. Another authority wrote that both the French and Allies lost 3,000 killed and wounded, while the French took 2,000 men, six guns and four colors. Chateau died from his wounds on 8 May 1814.
The victory failed to live up to Napoleon's expectations. He lamented, "The foe has enjoyed a stroke of rare good fortune, the heavy frosts permitted him to move over the fields – otherwise
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at least half his guns and transport would have been taken." In his disappointment he turned on his generals. After the battle when Victor complained to the emperor about losing his command, Napoleon unleashed a storm of abuse on his hapless subordinate. He also raged against Victor's wife who he accused of snubbing Empress Marie Louise. Victor managed to blunt his sovereign's fury by recalling their military exploits in Italy and by reminding Napoleon that his son-in-law Chateau lay dying. Finally, Napoleon relented and gave him the two Young Guard divisions of Charpentier and Joseph Boyer de Rebeval. Other generals who felt Napoleon's wrath at this time were Lhéritier for failing to charge
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at Valjouan, Jean François Aimé Dejean for not providing enough artillery ammunition and Claude-Étienne Guyot for losing some cannons.
Even before the battle started, Schwarzenberg ordered a general withdrawal to Troyes. He ordered Wrede to hold Bray until nightfall on 19 February and sent a dispatch to Blücher asking him to support his right flank at Méry-sur-Seine on 21 February. The Prussian replied that he would be at the rendezvous with 53,000 troops and 300 guns. With Montereau in French hands, the position of the Austrians on the left flank along the Loing River became precarious. Under the guise of negotiations with Allix, they retreated to join the wreckage of Schäffer's brigade at
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er became precarious. Under the guise of negotiations with Allix, they retreated to join the wreckage of Schäffer's brigade at Saint-Sérotin. Seslavin was ordered to relinquish his far left flank position and take a position on the opposite flank. Napoleon's pursuit was hampered by a lack of bridges and the Allies got a two-day head start in the march to Troyes. The next action between the two armies was at Méry-sur-Seine on 22 February.
# Battlefield Today.
Currently, part of this historic battle site near the village of Montereau-Fault-Yonne is being developed as a theme park celebrating the life of French Emperor Napoleon Bonaparte. The park, Napoleonland, is set for completion in 2017.
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Fulk, King of Jerusalem
Fulk (, or "Foulques"; c. 1089/92 – 13 November 1143), also known as Fulk the Younger, was the Count of Anjou (as Fulk V) from 1109 to 1129 and the King of Jerusalem from 1131 to his death. During his reign, the Kingdom of Jerusalem reached its largest territorial extent.
# Biography.
## Count of Anjou.
Fulk was born at Angers, between 1089 and 1092, the son of Count Fulk IV of Anjou and Bertrade de Montfort. In 1092, Bertrade deserted her husband and bigamously married King Philip I of France.
He became count of Anjou upon his father's death in 1109. In the next year, he married Ermengarde of Maine, cementing Angevin control over the County of Maine.
He was originally
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an opponent of King Henry I of England and a supporter of King Louis VI of France, but in 1118 or 1119 he had allied with Henry when he arranged for his daughter Matilda to marry Henry's son and heir, William Adelin. Fulk went on crusade in 1119 or 1120, and became attached to the Knights Templar (Orderic Vitalis). He returned, late in 1121, after which he began to subsidize the Templars, maintaining two knights in the Holy Land for a year. Much later, Henry arranged for his daughter Matilda to marry Fulk's son Geoffrey of Anjou, which she did in 1127 or 1128.
## Crusader and King.
By 1127 Fulk was preparing to return to Anjou when he received an embassy from King Baldwin II of Jerusalem.
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Baldwin II had no male heirs but had already designated his daughter Melisende to succeed him. Baldwin II wanted to safeguard his daughter's inheritance by marrying her to a powerful lord. Fulk was a wealthy crusader and experienced military commander, and a widower. His experience in the field would prove invaluable in a frontier state always in the grip of war.
However, Fulk held out for better terms than mere consort of the Queen; he wanted to be king alongside Melisende. Baldwin II, reflecting on Fulk's fortune and military exploits, acquiesced. Fulk abdicated his county seat of Anjou to his son Geoffrey and left for Jerusalem, where he married Melisende on 2 June 1129. Later Baldwin II
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bolstered Melisende's position in the kingdom by making her sole guardian of her son by Fulk, Baldwin III, born in 1130.
Fulk and Melisende became joint rulers of Jerusalem in 1131 with Baldwin II's death. From the start Fulk assumed sole control of the government, excluding Melisende altogether. He favored fellow countrymen from Anjou to the native nobility. The other crusader states to the north feared that Fulk would attempt to impose the suzerainty of Jerusalem over them, as Baldwin II had done; but as Fulk was far less powerful than his deceased father-in-law, the northern states rejected his authority. Melisende's sister Alice of Antioch, exiled from the Principality by Baldwin II, took
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control of Antioch once more after the death of her father. She allied with Pons of Tripoli and Joscelin II of Edessa to prevent Fulk from marching north in 1132; Fulk and Pons fought a brief battle before peace was made and Alice was exiled again.
In Jerusalem as well, Fulk was resented by the second generation of Jerusalem Christians who had grown up there since the First Crusade. These "natives" focused on Melisende's cousin, the popular Hugh II of Le Puiset, count of Jaffa, who was devotedly loyal to the Queen. Fulk saw Hugh as a rival, and it did not help matters when Hugh's own stepson accused him of disloyalty. In 1134, in order to expose Hugh, Fulk accused him of infidelity with Melisende.
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Hugh rebelled in protest. Hugh secured himself to Jaffa, and allied himself with the Muslims of Ascalon. He was able to defeat the army set against him by Fulk, but this situation could not hold. The Patriarch interceded in the conflict, perhaps at the behest of Melisende. Fulk agreed to peace and Hugh was exiled from the kingdom for three years, a lenient sentence.
However, an assassination attempt was made against Hugh. Fulk, or his supporters, were commonly believed responsible, though direct proof never surfaced. The scandal was all that was needed for the queen's party to take over the government in what amounted to a palace coup. Author and historian wrote that Fulk's supporters "went
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in terror of their lives" in the palace. Contemporary author and historian William of Tyre wrote of Fulk "he never attempted to take the initiative, even in trivial matters, without (Melisende's) consent". The result was that Melisende held direct and unquestioned control over the government from 1136 onwards. Sometime before 1136 Fulk reconciled with his wife, and a second son, Amalric was born.
## Securing the borders.
Jerusalem's northern border was of great concern. Fulk had been appointed regent of the Principality of Antioch by Baldwin II. As regent he had Raymond of Poitou marry the infant Constance of Antioch, daughter of Bohemund II and Alice of Antioch, and niece to Melisende. However,
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the greatest concern during Fulk's reign was the rise of Atabeg Zengi of Mosul.
In 1137 Fulk was defeated in battle near Baarin but allied with Mu'in ad-Din Unur, the vizier of Damascus. Damascus was also threatened by Zengi. Fulk captured the fort of Banias, to the north of Lake Tiberias and thus secured the northern frontier.
Fulk also strengthened the kingdom's southern border. His butler Paganus built the fortress of Kerak to the east of the Dead Sea, and to help give the kingdom access to the Red Sea, Fulk had Blanchegarde, Ibelin, and other forts built in the south-west to overpower the Egyptian fortress at Ascalon. This city was a base from which the Egyptian Fatimids launched frequent
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raids on the Kingdom of Jerusalem and Fulk sought to neutralise this threat.
In 1137 and 1142, Byzantine emperor John II Comnenus arrived in Syria attempting to impose Byzantine control over the crusader states. John's intention of making a pilgrimage, accompanied by his impressive army, to Jerusalem alarmed Fulk, who wrote to John pointing out that his kingdom was poor and could not support the passage of a large army. This lukewarm response dissuaded John from carrying through his intention, and he postponed his pilgrimage. John died before he could make good his proposed journey to Jerusalem.
## Death.
In 1143, while the king and queen were in Acre, Fulk was killed in a hunting accident.
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His horse stumbled, fell, and Fulk's skull was crushed by the saddle, "and his brains gushed forth from both ears and nostrils", as William of Tyre describes. He was carried back to Acre, where he lay unconscious for three days before he died. He was buried in the Church of the Holy Sepulchre in Jerusalem. Though their marriage started in conflict, Melisende mourned for him privately as well as publicly. Fulk was survived by his son Geoffrey of Anjou by his first wife, and Baldwin III and Amalric I by Melisende.
# Legacy.
## Depictions.
According to William, Fulk was ""a ruddy man, like David... faithful and gentle, affable and kind... an experienced warrior full of patience and wisdom in
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military affairs"." His chief fault was an inability to remember names and faces.
William of Tyre described Fulk as a capable soldier and able politician, but observed that Fulk did not adequately attend to the defense of the crusader states to the north. Ibn al-Qalanisi (who calls him "al-Kund Anjur", an Arabic rendering of "Count of Anjou") says that "he was not sound in his judgment nor was he successful in his administration." The Zengids continued their march on the crusader states, culminating in the fall of the County of Edessa in 1144, which led to the Second Crusade (see Siege of Edessa).
## Family.
In 1110, Fulk married Ermengarde of Maine (died 1126), the daughter of Elias I of
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Maine. Their four children were:
- 1. Geoffrey V of Anjou (1113–1151, father of Henry II of England.
- 2. Sibylla of Anjou (1112–1165, Bethlehem), married in 1123 William Clito (div. 1124), married in 1134 Thierry, Count of Flanders.
- 3. Matilda of Anjou (1106–1154, Fontevrault), married William Adelin; after his death in the White Ship disaster of 1120, she became a nun and later Abbess of Fontevrault.
- 4. Elias II of Maine (died 1151)
His second wife was Melisende, Queen of Jerusalem
- 1. Baldwin III of Jerusalem
- 2. Amalric I of Jerusalem
# Sources.
- Orderic Vitalis
- Robert of Torigny
- William of Tyre
- Runciman, Steven (1952) "A History of the Crusades, Vol. II: The Kingdom
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lda of Anjou (1106–1154, Fontevrault), married William Adelin; after his death in the White Ship disaster of 1120, she became a nun and later Abbess of Fontevrault.
- 4. Elias II of Maine (died 1151)
His second wife was Melisende, Queen of Jerusalem
- 1. Baldwin III of Jerusalem
- 2. Amalric I of Jerusalem
# Sources.
- Orderic Vitalis
- Robert of Torigny
- William of Tyre
- Runciman, Steven (1952) "A History of the Crusades, Vol. II: The Kingdom of Jerusalem," Cambridge University Press.
- Medieval Women, edited by Derek Baker, the Ecclesiastical History Society, 1978
- Payne, Robert. "The Dream and the Tomb", 1984
- "The Damascus Chronicle of Crusades", trans. H.A.R. Gibb, 1932.
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Hemiola
In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In pitch, "hemiola" refers to the interval of a perfect fifth. In rhythm, "hemiola" refers to three beats of equal value in the time normally occupied by two beats.
# Etymology.
The word "hemiola" comes from the Greek adjective ἡμιόλιος, "hemiolios", meaning "containing one and a half," "half as much again," "in the ratio of one and a half to one (3:2), as in musical sounds." The words "hemiola" and "sesquialtera" both signify the ratio 3:2, and in music were first used to describe relations of pitch. Dividing the string of a monochord in this ratio produces the interval of a perfect fifth.
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Beginning in the 15th century, both words were also used to describe rhythmic relationships, specifically the substitution (usually through the use of coloration—red notes in place of black ones, or black in place of "white", hollow noteheads) of three imperfect notes (divided into two parts) for two perfect ones (divided into three parts) in "tempus perfectum" or in "prolatio maior".
# Pitch.
## The perfect fifth.
"Hemiola" can be used to describe the ratio of the lengths of two strings as three-to-two (3:2), that together sound a perfect fifth. The early Pythagoreans, such as Hippasus and Philolaus, used this term in a music-theoretic context to mean a perfect fifth.
The justly tuned pitch
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ratio of a perfect fifth means that the upper note makes three vibrations in the same amount of time that the lower note makes two. In the cent system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents, or 2% of a semitone wider than seven semitones. The just perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds "in tune". Just perfect fifths are the basis of Pythagorean tuning, and are employed together with other just intervals in just intonation. The 3:2 just perfect fifth arises in the justly tuned C major scale between C and G.
## Other intervals.
Later
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Greek authors such as Aristoxenus and Ptolemy use the word to describe smaller intervals as well, such as the hemiolic chromatic "pyknon", which is one-and-a-half times the size of the semitone comprising the enharmonic "pyknon".
# Rhythm.
In rhythm, "hemiola" refers to three beats of equal value in the time normally occupied by two beats.
### sesquialtera.
"The Oxford Dictionary of Music" illustrates hemiola with a superimposition of three notes in the time of two and vice versa.
One textbook states that, although the word "hemiola" is commonly used for both simultaneous and successive durational values, describing a simultaneous combination of three against two is less accurate than
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for successive values and the "preferred term for a vertical two against three … is "sesquialtera"." "The New Harvard Dictionary of Music" states that in some contexts, a sesquialtera is equivalent to a hemiola. "Grove's Dictionary", on the other hand, has maintained from the first edition of 1880 down to the most recent edition of 2001 that the Greek and Latin terms are equivalent and interchangeable, both in the realms of pitch and rhythm, although David Hiley, E. Thomas Stanford, and Paul R. Laird hold that, though similar in effect, hemiola properly applies to a momentary occurrence of three duple values in place of two triple ones, whereas sesquialtera represents a proportional metric change
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between successive sections.
#### Sub-Saharan African music.
A repeating vertical hemiola is known as polyrhythm, or more specifically, cross-rhythm. The most basic rhythmic cell of sub-Saharan Africa is the 3:2 cross-rhythm. Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." Agawu states: "[The] resultant [3:2] rhythm holds the key to understanding ... there is no independence here, because 2 and 3 belong to a single Gestalt."
In the following example, a Ghanaian gyil plays a hemiola as the basis of an ostinato melody. The left hand (lower notes) sounds the two main beats, while the right
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hand (upper notes) sounds the three cross-beats.
#### European music.
In compound time ( or ). Where a regular pattern of two beats to a measure is established at the start of a phrase. This changes to a pattern of three beats at the end of the phrase.
The minuet from J. S. Bach's keyboard Partita No. 5 in G major articulates groups of 2 times 3 quavers that are really in time, despite the metre stated in the initial time-signature . The latter time is restored only at the cadences (bars 4 and 11–12):
Later in the same piece, Bach creates a conflict between the two metres ( against ):
Hemiola is found in many Renaissance pieces in triple rhythm. One composer who exploited this characteristic
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was the 16th-century French composer Claude Le Jeune, a leading exponent of musique mesurée à l'antique. One of his best-known chansons is "Revoici venir du printemps" , where the alternation of compound-duple and simple-triple metres with a common counting unit for the beat subdivisions can be clearly heard:
The hemiola was commonly used in baroque music, particularly in dances, such as the courante and minuet. Other composers who have used the device extensively include Corelli, Handel, Weber and Beethoven. A spectacular example from Beethoven comes in the scherzo from his String Quartet No. 6. As Philip puts it, "The constant cross-rhythms shifting between and , commoner at certain earlier
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and later periods, were far from usual in 1800, and here they are made to sound especially eccentric owing to frequent sforzandi on the last quaver of the bar... it looks ahead to later works and must have sounded very disconcerting to contemporary audiences."
Later in the nineteenth century, Tchaikovsky frequently used hemiolas in his waltzes, as did Richard Strauss in the waltzes from "Der Rosenkavalier", and the third movement of Robert Schumann's Piano Concerto is noted for the ambiguity of its rhythm. John Daverio says that the movement's "fanciful hemiolas... serve to legitimize the dance-like material as a vehicle for symphonic elaboration." Johannes Brahms was particularly famous for
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exploiting the hemiola's potential for large-scale thematic development. Writing about the rhythm and meter of Brahms's Symphony No. 3, says "Perhaps in no other first movement by Brahms does the development of these elements play so critical a role. The first movement of the third is cast in meter that is also open, through internal recasting as (a so-called hemiola). Metrical ambiguity arises in the very first appearance of the motto [opening theme]."
At the beginning of the second movement, , of his String Quartet (1903), Ravel "uses the "pizzicato" as a vehicle for rhythmic interplay between and ."
## Horizontal hemiola.
Peter Manuel, in the context of an analysis of the Flamenco soleá
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song form, refers to the following figure as a "horizontal hemiola" or "sesquialtera" (which he translates as if it were Spanish rather than Latin: "six that alters"). It is "a cliché of various Spanish and Latin American musics ... well established in Spain since the sixteenth century", a twelve-beat scheme with internal accents, consisting of a bar followed by one in , for a 3 + 3 + 2 + 2 + 2 pattern.
This figure is a common African bell pattern, used by the Hausa people of Nigeria, in Haitian Vodou drumming, Cuban palo, and many other drumming systems. The figure is also used in many sub-varieties of the Flamenco genre (bulerías, for example), and in various popular Latin American musics..
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ar Latin American musics.. It is also a fundamental feature of the Czech furiant dance form, familiar from the two examples in Dvořák's Slavonic Dances Op. 48. The horizontal hemiola suggests metric modulation ( changing to ). This interpretational switch has been exploited, for example, by Leonard Bernstein, in the song "America" from "West Side Story", as can be heard in the prominent motif (suggesting a duple beat scheme, followed by a triple beat scheme):
# See also.
- Syncopation
# Further reading.
- Brandel, Rose (1959). "The African Hemiola Style", "Ethnomusicology", 3(3):106–17, correction, 4(1):iv.
- Károlyi, Ottó (1998). "Traditional African & Oriental Music", Penguin Books. .
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Moment of inertia
The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation rate. It is an extensive (additive) property: for a point mass the moment of inertia is just the mass times the square of the perpendicular distance to the rotation axis. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its
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component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other.
# Introduction.
When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any
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given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram meter squared (kg·m) in SI units and pound-foot-second squared (lbf·ft·s) in imperial or US units.
Moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics - both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by formula_1, where formula_2 is the distance of the
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point from the axis, and formula_3 is the mass. For an extended rigid body, the moment of inertia is just the sum of all the small pieces of mass multiplied by the square of their distances from the axis in question. For an extended body of a regular shape and uniform density, this summation sometimes produces a simple expression that depends on the dimensions, shape and total mass of the object.
In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, known as a compound pendulum. The term "moment of inertia" was introduced by Leonhard Euler in his book "Theoria motus corporum solidorum seu rigidorum" in 1765, and it is incorporated
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into Euler's second law.
The natural frequency of oscillation of a compound pendulum is obtained from the ratio of the torque imposed by gravity on the mass of the pendulum to the resistance to acceleration defined by the moment of inertia. Comparison of this natural frequency to that of a simple pendulum consisting of a single point of mass provides a mathematical formulation for moment of inertia of an extended body.
Moment of inertia also appears in momentum, kinetic energy, and in Newton's laws of motion for a rigid body as a physical parameter that combines its shape and mass. There is an interesting difference in the way moment of inertia appears in planar and spatial movement. Planar
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movement has a single scalar that defines the moment of inertia, while for spatial movement the same calculations yield a 3 × 3 matrix of moments of inertia, called the inertia matrix or inertia tensor.
The moment of inertia of a rotating flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. The moment of inertia of an airplane about its longitudinal, horizontal and vertical axis determines how steering forces on the control surfaces of its wings, elevators and tail affect the plane in roll, pitch and yaw.
# Definition.
Moment of inertia formula_4 is defined as the ratio of the net angular momentum formula_5 of a system to its angular velocity
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formula_6 around a principal axis, that is
If the angular momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their outstretched arms or divers curl their bodies into a tuck position during a dive, to spin faster.
If the shape of the body does not change, then its moment of inertia appears in Newton's law of motion as the ratio of an applied torque formula_8 on a body to the angular acceleration formula_9 around a principal axis, that is
For a simple pendulum, this definition yields a formula for the moment of inertia formula_4 in terms of the mass formula_3 of the pendulum and its
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distance formula_2 from the pivot point as,
Thus, moment of inertia depends on both the mass formula_3 of a body and its geometry, or shape, as defined by the distance formula_2 to the axis of rotation.
This simple formula generalizes to define moment of inertia for an arbitrarily shaped body as the sum of all the elemental point masses formula_17 each multiplied by the square of its perpendicular distance formula_2 to an axis formula_19.
In general, given an object of mass formula_3, an effective radius formula_19 can be defined for an axis through its center of mass, with such a value that its moment of inertia is
where formula_19 is known as the radius of gyration.
# Examples.
## Simple
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pendulum.
Moment of inertia can be measured using a simple pendulum, because it is the resistance to the rotation caused by gravity. Mathematically, the moment of inertia of the pendulum is the ratio of the torque due to gravity about the pivot of a pendulum to its angular acceleration about that pivot point. For a simple pendulum this is found to be the product of the mass of the particle formula_3 with the square of its distance formula_2 to the pivot, that is
This can be shown as follows: The force of gravity on the mass of a simple pendulum generates a torque formula_27 around the axis perpendicular to the plane of the pendulum movement. Here formula_28 is the distance vector perpendicular
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to and from the force to the torque axis, and formula_29 is the net force on the mass. Associated with this torque is an angular acceleration, formula_30, of the string and mass around this axis. Since the mass is constrained to a circle the tangential acceleration of the mass is formula_31. Since formula_32 the torque equation becomes:
where formula_34 is a unit vector perpendicular to the plane of the pendulum. (The second to last step uses the vector triple product expansion with the perpendicularity of formula_30 and formula_28.) The quantity formula_37 is the "moment of inertia" of this single mass around the pivot point.
The quantity formula_37 also appears in the angular momentum of
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a simple pendulum, which is calculated from the velocity formula_39 of the pendulum mass around the pivot, where formula_40 is the angular velocity of the mass about the pivot point. This angular momentum is given by
using a similar derivation to the previous equation.
Similarly, the kinetic energy of the pendulum mass is defined by the velocity of the pendulum around the pivot to yield
This shows that the quantity formula_37 is how mass combines with the shape of a body to define rotational inertia. The moment of inertia of an arbitrarily shaped body is the sum of the values formula_1 for all of the elements of mass in the body.
## Compound pendulum.
A compound pendulum is a body formed
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from an assembly of particles of continuous shape that rotates rigidly around a pivot. Its moment of inertia is the sum of the moments of inertia of each of the particles that it is composed of. The natural frequency (formula_45) of a compound pendulum depends on its moment of inertia, formula_46,
where formula_3 is the mass of the object, formula_49 is local acceleration of gravity, and formula_2 is the distance from the pivot point to the center of mass of the object. Measuring this frequency of oscillation over small angular displacements provides an effective way of measuring moment of inertia of a body.
Thus, to determine the moment of inertia of the body, simply suspend it from a convenient
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pivot point formula_51 so that it swings freely in a plane perpendicular to the direction of the desired moment of inertia, then measure its natural frequency or period of oscillation (formula_52), to obtain
where formula_52 is the period (duration) of oscillation (usually averaged over multiple periods).
The moment of inertia of the body about its center of mass, formula_55, is then calculated using the parallel axis theorem to be
where formula_3 is the mass of the body and formula_2 is the distance from the pivot point formula_51 to the center of mass formula_60.
Moment of inertia of a body is often defined in terms of its "radius of gyration", which is the radius of a ring of equal mass
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around the center of mass of a body that has the same moment of inertia. The radius of gyration formula_19 is calculated from the body's moment of inertia formula_55 and mass formula_3 as the length
### Center of oscillation.
A simple pendulum that has the same natural frequency as a compound pendulum defines the length formula_5 from the pivot to a point called the center of oscillation of the compound pendulum. This point also corresponds to the center of percussion. The length formula_5 is determined from the formula,
or
The seconds pendulum, which provides the "tick" and "tock" of a grandfather clock, takes one second to swing from side-to-side. This is a period of two seconds, or a
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natural frequency of formula_69 for the pendulum. In this case, the distance to the center of oscillation, formula_5, can be computed to be
Notice that the distance to the center of oscillation of the seconds pendulum must be adjusted to accommodate different values for the local acceleration of gravity. Kater's pendulum is a compound pendulum that uses this property to measure the local acceleration of gravity, and is called a gravimeter.
# Measuring moment of inertia.
The moment of inertia of a complex system such as a vehicle or airplane around its vertical axis can be measured by suspending the system from three points to form a trifilar pendulum. A trifilar pendulum is a platform supported
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by three wires designed to oscillate in torsion around its vertical centroidal axis. The period of oscillation of the trifilar pendulum yields the moment of inertia of the system.
# Motion in a fixed plane.
## Point mass.
The moment of inertia about an axis of a body is calculated by summing formula_1 for every particle in the body, where formula_2 is the perpendicular distance to the specified axis. To see how moment of inertia arises in the study of the movement of an extended body, it is convenient to consider a rigid assembly of point masses. (This equation can be used for axes that are not principal axes provided that it is understood that this does not fully describe the moment of inertia.)
Consider
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the kinetic energy of an assembly of formula_74 masses formula_75 that lie at the distances formula_76 from the pivot point formula_51, which is the nearest point on the axis of rotation. It is the sum of the kinetic energy of the individual masses,
This shows that the moment of inertia of the body is the sum of each of the formula_1 terms, that is
Thus, moment of inertia is a physical property that combines the mass and distribution of the particles around the rotation axis. Notice that rotation about different axes of the same body yield different moments of inertia.
The moment of inertia of a continuous body rotating about a specified axis is calculated in the same way, except with infinitely
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many point particles. Thus the limits of summation are removed, and the sum is written as follows:
Another expression replaces the summation with an integral,
Here, the function formula_83 gives the mass density at each point formula_84, formula_28 is a vector perpendicular to the axis of rotation and extending from a point on the rotation axis to a point formula_84 in the solid, and the integration is evaluated over the volume formula_87 of the body formula_88. The moment of inertia of a flat surface is similar with the mass density being replaced by its areal mass density with the integral evaluated over its area.
Note on second moment of area: The moment of inertia of a body moving in
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a plane and the second moment of area of a beam's cross-section are often confused. The moment of inertia of a body with the shape of the cross-section is the second moment of this area about the formula_89-axis perpendicular to the cross-section, weighted by its density. This is also called the "polar moment of the area", and is the sum of the second moments about the formula_90- and formula_91-axes. The stresses in a beam are calculated using the second moment of the cross-sectional area around either the formula_90-axis or formula_91-axis depending on the load.
### Examples.
The moment of inertia of a compound pendulum constructed from a thin disc mounted at the end of a thin rod that oscillates
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around a pivot at the other end of the rod, begins with the calculation of the moment of inertia of the thin rod and thin disc about their respective centers of mass.
/math
where formula_94 is the mass of the rod.
where formula_101 is its mass.
where formula_5 is the length of the pendulum. Notice that the parallel axis theorem is used to shift the moment of inertia from the center of mass to the pivot point of the pendulum.
A list of moments of inertia formulas for standard body shapes provides a way to obtain the moment of inertia of a complex body as an assembly of simpler shaped bodies. The parallel axis theorem is used to shift the reference point of the individual bodies to the reference
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point of the assembly.
As one more example, consider the moment of inertia of a solid sphere of constant density about an axis through its center of mass. This is determined by summing the moments of inertia of the thin discs that form the sphere. If the surface of the ball is defined by the equation
then the radius formula_2 of the disc at the cross-section formula_89 along the formula_89-axis is
Therefore, the moment of inertia of the ball is the sum of the moments of inertia of the discs along the formula_89-axis,
where formula_112 is the mass of the sphere.
## Rigid body.
If a mechanical system is constrained to move parallel to a fixed plane, then the rotation of a body in the system
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occurs around an axis formula_34 perpendicular to this plane. In this case, the moment of inertia of the mass in this system is a scalar known as the "polar moment of inertia". The definition of the polar moment of inertia can be obtained by considering momentum, kinetic energy and Newton's laws for the planar movement of a rigid system of particles.
If a system of formula_114 particles, formula_115, are assembled into a rigid body, then the momentum of the system can be written in terms of positions relative to a reference point formula_116, and absolute velocities formula_117:
where formula_40 is the angular velocity of the system and formula_120 is the velocity of formula_116.
For planar
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movement the angular velocity vector is directed along the unit vector formula_122 which is perpendicular to the plane of movement. Introduce the unit vectors formula_123 from the reference point formula_116 to a point formula_125, and the unit vector formula_126, so
This defines the relative position vector and the velocity vector for the rigid system of the particles moving in a plane.
Note on the cross product: When a body moves parallel to a ground plane, the trajectories of all the points in the body lie in planes parallel to this ground plane. This means that any rotation that the body undergoes must be around an axis perpendicular to this plane. Planar movement is often presented as
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