query: Why is kinetic energy defined as $(1/2)m v^2$?
positive_passages.docid: 146358
positive_passages.text: Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?
negative_passages.docid: 141474
negative_passages.text: Prove the Total Mechanical Energy of the System is Conserved via Differential Equations
negative_passages.docid: 122561
negative_passages.text: Is the energy always discrete?
negative_passages.docid: 119880
negative_passages.text: Integrating factor $1/T$ in 2nd Law of Thermodynamics
negative_passages.docid: 45613
negative_passages.text: Conservation of energy when slowing an object down
negative_passages.docid: 58605
negative_passages.text: Landau's derivation of a free particle's kinetic energy- expansion of a function?
negative_passages.docid: 125883
negative_passages.text: Moment of inertia: why $\mathrm{dI}=r^2\mathrm{dm}$ instead of $\mathrm{dI}=m\mathrm{dr^2}$?
negative_passages.docid: 12818
negative_passages.text: In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter?
negative_passages.docid: 112073
negative_passages.text: What does a Lagrangian of the form $L=m^2\dot x^4 +U(x)\dot x^2 -W(x)$ represent?
negative_passages.docid: 40028
negative_passages.text: Calculating Energy of a Wave
negative_passages.docid: 7477
negative_passages.text: Why is the momentum of a particle $\gamma mv$?
negative_passages.docid: 86401
negative_passages.text: How has the definition of gravitational potential energy been derived?
negative_passages.docid: 131167
negative_passages.text: Kinetic energy of the object, but Potential energy of the system: Why is it so?
negative_passages.docid: 124744
negative_passages.text: Conservation of $\vec{p}$ in Ballistic pendulum
negative_passages.docid: 26085
negative_passages.text: Why is the action dimensionless in natural units?
negative_passages.docid: 93539
negative_passages.text: Why is $M\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ correct and $(M - dm)\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ wrong?
negative_passages.docid: 56266
negative_passages.text: Potential energy and the work energy theorem