A uniforum stick AB of mass M and length L is moving on a smooth plane with speed v. The motion is normal to the stick. The stick collides with a fixed nail on the plane and impact is at the middle of AC, where C is the C.M. of the stick. Q: What is the instantaneous speed of the C.M. of the stick? The attempt at a solution: Let F be the force between the stick and the nail vf be the instantaneous speed of the C.M. of the stick ω be the angular velocity of the stick after impact △P = F△t M(vf - v)= F△t Take moment @ C ∴ I=1/12 ML^2 △L (angular momentum) = τ(torque)△t ∵τ= rXF ∴I(ω-0)= (L/4)F△t (1/12 ML^2)ω = (L/4) M(vf - v) ... (vf - v) = 1/3 Lω How can I let ω interms of v or vf ? Or..Is there anything I have missed?