Question

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this collision

A)	the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.
B)	the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar.
C)	the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system.
D)	both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.
E)	both the linear momentum and the angular momentum of the system (ball and bar) are conserved.

Answer 1

Concepts and reason

The concept of inelastic collision is required to solve the problem.

Initially, find out the type of collision elastic or inelastic. Later, check whether the angular momentum is conserved or not by determining the net torque acting on the system. Finally, check whether the linear momentum is conserved or not by determining the net force acting on the system.

Fundamentals

Collision is of two types elastic collision and inelastic collision. Elastic collision is defined as the collision in which both momentum and kinetic energy are conserved. Inelastic collision is defined as the collision in which momentum is conserved but kinetic energy is not conserved.

Inelastic collision is defined as the collision in which momentum is conserved but kinetic energy is not conserved.

The collision in which the colliding objects stick together after the collision is inelastic collision. As the ball is stick to the bar, the collision is inelastic and kinetic energy is not conserved in inelastic collision. Hence, the statement that both the angular momentum of the system and its kinetic energy are conserved is wrong.

Hook exerts a force on the bar which implies that the net force acting on the system is not zero. Hence, linear momentum is not conserved. Therefore, the statement that both the linear momentum and the angular momentum of the system are conserved is wrong.

The hook and gravity do not exert any torque on the system about the hook. Therefore, as the net torque acting on the system about the hook is zero, the angular momentum of the system is conserved about the hook.

Hence, the statements that the angular momentum of the system is not conserved because the hook exerts a force on the bar and the angular momentum is conserved about the hook because only gravity is acting on the system are wrong.

Net torque acting on the system is equal to the rate of change of angular momentum. As the hook and the gravity do not exert any torque on the system about the hook, the net torque acting on the system about the hook is zero. Hence, the angular momentum of the system is conserved about the hook.

Hence, the statement that the angular momentum of the system is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook is true.

Ans:

The angular momentum of the system is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.