Chapter 9, Problem 1STP

To determine

To choose: The correct option.

Answer to Problem 1STP

The correct option (B), I decreases, L stays constant and $\omega$ increases.

Explanation of Solution

Introduction:

Moment of inertia depends directly on the mass and square of the distance from axis of rotation.

As per conservation of angular momentum, in the absence of net external torque, the angular momentum of the object remains unchanged.

Angular velocity depends inversely on the moment of inertia of the object when no net torque acts on the object.

As the star collapse, the distance from the axis of rotation decrease. Since the moment of inertia depend directly on the distance from the axis of rotation, hence the moment of inertia of the collapsing star decrease.

The star collapse on its own and no external torque acts on it. Hence, the angular momentum of the collapsing star remains unchanged.

It is known that angular velocity depends inversely on the moment of inertia of the object when no net torque acts on the object. Since net torque acting on the collapsing star is zero, the angular velocity of the star changes inversely relative to its moment of inertia. As the moment of inertia of collapsing star decrease, the angular velocity must increase.

Hence, the moment of inertia decrease, angular momentum remains unchanged and angular velocity increase.

Conclusion:

Therefore, the correct option is (B).