Angular momentum $L=I\omega$, in kg.m²/s

Compare with $p = m v$

Rewrite N2L for rotations as \[ {\tau} = \lim_{\Delta t \rightarrow 0} {{\Delta {L}}\over{\Delta t}} \quad \mbox{or} \quad \sum {\tau}_{\rm ext} = \lim_{\Delta t \rightarrow 0} {{\Delta {L}_{\rm total}}\over{\Delta t}} \] or as the law of conservation of angular momentum \[ \sum {\tau}_{ext} = 0 \quad \rightarrow \quad L=\mbox{const} \quad \rightarrow \quad I_f\omega_f = I_i\omega_i \] Note that the rotational K.E., \(K_{\rm rot} = \frac{1}{2} I\omega^2\) does change: \[ K_{f} = \frac{1}{2} I_f\omega_f^2 = \frac{1}{2} \frac{(I_f\omega_f)^2}{I_f} = \frac{1}{2} \frac{(I_i\omega_i)^2}{I_f} = \frac{1}{2} I_i\omega_i^2 \, \frac{I_i}{I_f} = K_{i} \, \frac{I_i}{I_f} \]