Rotational dynamics

Moment of inertia and angular momentum

Every linear quantity has a rotational partner: mass → moment of inertia $I=\sum mr^2$, force → torque $T$, momentum → angular momentum $L=I\omega$. Newton's second law becomes $T=I\alpha$; kinetic energy is $\frac12I\omega^2$; power is $T\omega$. With no external torque, angular momentum is conserved.