Kinetic Energy#
Definition: Kinetic Energy
The kinetic energy of a point mass \(m\) is defined as one-half of the product of \(m\) and its speed squared:
\[ \frac{1}{2}mv^2 \]
The (total) kinetic energy of a continuous mass distribution \(\rho\) with volume \(V\) is the integral
\[ \int_V \rho(\boldsymbol{r}) v(\boldsymbol{r})^2 \mathop{\mathrm{d}V}, \]
where \(v(\boldsymbol{r})\) is the velocity of the infinitesimally small point mass located at \(\boldsymbol{r}\).
The (total) kinetic energy of a physical system is the sum of the kinetic energies of its components.
Notation
\[ K \qquad E_{\text{k}} \qquad E_{\text{kin}} \]