Question

A rod of length 2d0 and mass 2m0 is at rest on a flat, horizontal surface. One end of the rod is connected to a pivot that the rod will rotate around if acted upon by a net torque. A sphere of mass m0 is launched horizontally toward the free end of the rod with velocity v0, as shown in the figure. After the sphere collides with the rod, the sphere sticks to the rod and both objects rotate around the pivot with a common angular velocity. Which of the following predictions is correct about angular momentum and rotational kinetic energy of the sphere-rod system immediately before the collision and immediately after the collision?.

Answer 1

The angular momentum immediately before and after the collision is equal. The rotational kinetic energy before the collision is greater than the rotational kinetic energy after the collision.

What are rotational kinetic energy and angular momentum?

When a body is rotating in a plane about a center, the energy possessed by the body is known as rotational kinetic energy.

Angular momentum is the momentum of a body having circular motion.

According to the law of conservation of angular momentum, the momentum remains conserved before and after the collision.

In the given sphere rod system, after the sphere (m0) sticks to the rod(2m0), the mass increases to 3m0 due to which the moment of inertia is increased but the speed is decreased.

Rotational Kinetic Energy =$\frac{1}{2}$Iω²

Thus, the angular momentum immediately before and after the collision is equal. The rotational kinetic energy before the collision is greater than the rotational kinetic energy after the collision.

Learn more about rotational kinetic energy and angular momentum.

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