Yet another problem I'm breaking my head with: A thin rod of mass M and length L is suspended vertically from a frictionless pivot at its upper end. A mass m of putty traveling horizontally with a speed v strikes the rod at its center of mass and sticks there. How high does the bottom of the rod swing? I can't apply conservation of momentum because of gravity. The collision is inelastic so kinectic energy isn't conserved. This just leaves me with using torques and potential energy. I figured I could calculate the work done by the torque due to gravity and then equate this with the change in potential energy but then my answer will be independent of v which suggests that my reasoning is bogus. What other things can I look at?