11.2: Kinetic energy of a rigid body
As will be derived in Sec. 11.6, the kinetic energy of a rigid body \(C\) can be written as a sum of a translational component \(T_{C \text {, trans }}\) due to the speed \(\overrightarrow{\boldsymbol{v}}_{G}\) of the \(\mathrm{CoM}\) and a rotational component \(T_{C, \text { rot }}\) due to its angular velocity \(\omega_{C}\).
\[\begin{align} T_{C, 2 D} & =T_{C, \text { trans }}+T_{C, \text { rot }, 2 D} \tag{11.12} \label{11.12}\\[4pt] T_{C, \text { trans }} & =\frac{1}{2} m_{\mathrm{tot}}\left|\overrightarrow{\boldsymbol{v}}_{G}\right|^{2} \tag{11.13} \label{11.13}\\[4pt] T_{C, \text { rot }, 2 D} & =\frac{1}{2} I_{G, z z} \omega_{C}^{2} \tag{11.14} \label{11.14}\end{align}\]