A uniform rod of mass M and length d is initially at rest on a horizontal and frictionless table contained in the xy plane, the plane of the screen. The rod is free to rotate about an axis perpendicular to the plane and passing through the pivot point at a distance d/3 measured from one of its ends. A small point mass m, moving with speed v0, hits the rod and stick to it at the point of impact at a distance d/3 from the pivot.

Question

A uniform rod of mass M and length d is initially at rest on a horizontal and frictionless table contained in the xy plane, the plane of the screen. The rod is free to rotate about an axis perpendicular to the plane and passing through the pivot point at a distance d/3 measured from one of its ends. A small point mass m, moving with speed v0, hits the rod and stick to it at the point of impact at a distance d/3 from the pivot.

a. If the mass of the rod is M=4m, what is the magnitude of the angular velocity of the rod+small mass system after the collision?

b. Using again M=4m. What is the speed of the center of mass of the rod right after collision?

Damon · Answer

angular momentum of the entire system (rod and particle) around the pivot point is the same before and after. There are no external torques about that point. (Of course before the crash it is just m Vo times distance d/3 between pivot point and crash point.)