NOTE 1 The kinetic energy of a body is given by the integral ${\displaystyle T=\frac{1}{2}{\displaystyle {\int }_{\text{D}}{v}^2}dm}$, where D is a domain containing the body. When the axis of rotation is through the centre of mass, T is also given by ${\displaystyle T=\frac{1}{2}{m}_{\text{t}}{v}_{\text{G}}^2+\frac{1}{2}J{\omega }^2}$, where m_t is total mass, V_G is speed of the centre of mass, J is moment of inertia relative to the axis of rotation, and ω is the magnitude of the angular velocity, and where v_G, J, and ω can be time-dependent.

NOTE 2 In relativity, the dependence of the mass m on the speed v has to be considered.