A wheel is rotating freely about a vertical axis with constant angular velocity. Small parts of the wheel come loose and fly off. How does this affect the rotational speed of the wheel? Is angular momentum conserved? Is kinetic energy conserved? Explain.

Solutions

VerifiedIn order to answer this question, we will need first Newton's law which says that the pieces of the wheel that fly off will carry their share of angular momentum. This means that the angular velocity will remain the same since the angular momentum will decrease due to the moment of inertia decrease. The rotational kinetic energy will not be conserved as well as the translational kinetic energy.

The rotational speed of the wheel will not change. Angular momentum of the entire system is conserved, since no net torque operates on the wheel. The small parts of the wheel that fly off will carry angular momentum with them

**Problem Definition and Givens:**

We are given a wheel that rotates around a vertical axis, it is given that the rotation is **free** rotation.

At a point, some of the parts of the wheel flew off of the system because they got loose.

We need to explain how this will affect the system rotational speed.

Also, we need to determine whether the angular momentum and the kinetic energy would be conserved or not.