Home > Courses > 1P21_Sternin > LinearAngularMomentum Angular momentum 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: $K_{f} = \frac{1}{2} I_f\omega_f^2 = \frac{1}{2} \frac{(I_f\omega_f)^2}{I_f} = \frac{1}{2} \frac{(I_i\omega_i)^2}{I_f} = \frac{1}{2} I_i\omega_i^2 \, \frac{I_i}{I_f} = K_{i} \, \frac{I_i}{I_f}$