# Conservation of angular momentum in an inelastic collision

I have a question about the second method used to solve the problem above.

The moment of inertia with respect to the stick's midpoint after the collision is $$ml^2/12 + ml^2/4$$ or $$ml^2/3$$ so the angular momentum with respect to the stick's center after the collision is $$ml^2/3*w$$. Therefore, equation 8.56 becomes $$mv_0l/2 = ml^2/3*w$$ but this doesn't give the same w value. Can someone explain why?

• Your question is really about (8.54) and if $I_{\rm CM}$ is $\frac{m}{3} \ell^2$ or $\frac{5 m}{24} \ell^2$. The rest is just confusing the issue here. Sep 14, 2021 at 22:35

Instead of all the parts moving with speed proportional to $$r$$ as the distance from your axis, the parts are moving with various speeds as it spins around the center of mass.