A uniform thin rod (M = 5.12 kg, L = 5.2 m) sits motionless on a horizontal, frictionless table (as in the previous problem). Now, however, it is pinned to the table by a frictionless hinge placed distance x = 1.75 m above the center of mass, and the rod is free to rotate about the hinge. A point particle of mass m = 0.216 kg) moves at speed vo = 72.9 m/s and strikes the rod on the end below the center of mass, and perpendicular to the rod.
a) Suppose the block is made of clay, and it sticks to the rod. Find ω, the angular speed of the clay-plus-rod after the collision.
b) Suppose the block is made of steel; it hits the rod and comes to a complete stop without sticking to the rod. Find ω, the angular speed of the rod after the collision.