Kinetics in Rotation

page=279 Given a rigid body of $N$ particles, we have angular momentum for particle $k$ about the center of mass __ is given by

$${\vec{h}}_{k/c}={\vec{r}}_{k/c}\times m_k{\vec{v}}_k$$

And

$$\begin{array}{rl}\frac{d}{dt}{\vec{h}}_{k/c}& ={\vec{v}}_{k/c}\times m_k{\vec{v}}_k+{\vec{r}}_{k/c}\times m_k{\vec{a}}_k\\ \frac{d}{dt}{\vec{h}}_{k/c}& =-{\vec{v}}_c\times m_k{\vec{v}}_k+{\vec{r}}_{k/c}\times m_k{\vec{a}}_k\\ \frac{d}{dt}{\vec{h}}_{k/c}& =-\sum _k{\vec{v}}_c\times m_k{\vec{v}}_k+{\vec{r}}_{k/c}\times m_k{\vec{a}}_k\\ \frac{d}{dt}{\vec{h}}_{k/c}& ={\vec{T}}_c\end{array}$$

Using that $F\vec{r}=T$ is the Angular Momentum