A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller?

1.Its angular velocity decreases.
2.Its angular momentum increases.
3.Its angular velocity remains constant.
4. Its angular momentum remains constant.
5. Both its angular momentum and its angular velocity remain constant.

To determine what happens as a spinning star collapses under its own gravitational pull, we need to consider the principle of conservation of angular momentum.

Angular momentum is a property of rotating objects and is given by the product of the moment of inertia and the angular velocity of the object. According to the conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque.

As the spinning star collapses, its moment of inertia changes due to the redistribution of mass. The moment of inertia is a measure of how mass is distributed relative to the axis of rotation. The collapse causes the star to become smaller and typically results in a decrease in the moment of inertia.

Since the angular momentum is conserved, if the moment of inertia decreases, the star's angular velocity must increase to compensate and keep the total angular momentum constant. This means that option 1, "Its angular velocity decreases," is incorrect.

On the other hand, option 2, "Its angular momentum increases," is also incorrect because the conservation of angular momentum implies that the total angular momentum remains constant.

Option 3, "Its angular velocity remains constant," is also incorrect since the decrease in moment of inertia requires an increase in angular velocity to maintain angular momentum.

Similarly, option 4, "Its angular momentum remains constant," is incorrect because the change in moment of inertia necessitates a change in angular velocity.

The correct answer is option 5, "Both its angular momentum and its angular velocity remain constant." This is because the decrease in moment of inertia is exactly compensated by an increase in angular velocity, resulting in a conserved angular momentum.

As a spinning star collapses under its own gravitational pull, two factors related to its rotation are involved: angular velocity and angular momentum.

Angular velocity refers to the rate at which the star spins, while angular momentum is a measure of the star's rotational motion.

When a spinning star collapses, its radius decreases, causing its moment of inertia to decrease. According to the conservation of angular momentum, a decrease in the moment of inertia must be compensated for by an increase in angular velocity to keep the angular momentum constant.

Therefore, the correct answer is option 3: Its angular velocity remains constant.