In what circumstances can the angular velocity of system of particles change without any change in the system\'s angular momentum?


This cannot happen under any circumstances.

This can happen if an external net torque is applied properly to the system.

This can happen if the only forces acting are internal to the system.

This can happen if a net external force acts on the system\'s center of mass.

This can happen if the only forces acting are internal to the system.

Think, spinning figure skater pulls arms in and spins faster

ang momentum L = I omega
for simple dumbell = m r^2 omega
decrease r ----> increase omega for same L

This can happen if the only forces acting are internal to the system

This can happen if the only forces acting are internal to the system.

The correct answer is "This can happen if the only forces acting are internal to the system."

To understand why, let's break down the question and the concepts involved.

Angular velocity is a measure of how fast an object is rotating around a fixed axis. It is defined as the change in angular displacement over time. It is typically symbolized by the Greek letter omega (ω).

Angular momentum, on the other hand, is a measure of an object's tendency to keep rotating around a fixed axis. It is defined as the product of an object's moment of inertia (I) and its angular velocity (ω). It is typically symbolized by the letter L.

According to the principle of conservation of angular momentum, the total angular momentum of a system remains constant if no external torques act on the system. In other words, if the net torque on a system is zero, its angular momentum will remain constant.

So, in the given question, we are asked about a scenario where the angular velocity of a system of particles changes without any change in the system's angular momentum.

If an external net torque is applied properly to the system, it will cause a change in the system's angular momentum. This is because a torque produces a change in an object's angular momentum by causing it to rotate or change its rate of rotation.

If a net external force acts on the system's center of mass, it will also cause a change in the system's angular momentum. This is because a force acting at the center of mass results in both translational motion and rotational motion, thus affecting the system's angular momentum.

However, the correct answer is "This can happen if the only forces acting are internal to the system." In this situation, the internal forces exerted by particles within the system cancel each other out, resulting in no net external torque on the system. As a result, even though the angular velocity may change due to the internal forces, the total angular momentum of the system will remain constant.