Translational Kinetic Energy

The translational kinetic energy of a collection of masses $m_i$ is given by

$$E_K \eqsp \frac{1}{2} M v_c^2$$

where $M=\sum_i m_i$ is the total mass, and $v_c$ denotes the speed of the center-of-mass. We have $v_c\isdeftext \left\Vert\,\underline{v}_c\,\right\Vert$ , where $\underline{v}_c$ is the velocity of the center of mass.

More generally, the total energy of a collection of masses (including distributed and/or rigidly interconnected point-masses) can be expressed as the sum of the translational and rotational kinetic energies [272, p. 98].