Question:

A 2 kg mass is attached to a string and allowed to move in a circle of radius 0.5 m. The mass is moving at a constant speed of 4 m/s. Determine the angular momentum of the mass about the center of the circle and explain how conservation of angular momentum applies in this scenario.

Answer:

The angular momentum of an object rotating in a circle can be calculated using the formula:

Where:

• $L$ = Angular momentum
• $m$ = Mass of the object
• $v$ = Velocity of the object
• $r$ = Radius of the circle

Plugging in the given values:

We can calculate the angular momentum:

The conservation of angular momentum states that if no external torque (or moment of force) is applied to a rotating system, the angular momentum of the system remains constant. In this scenario, the mass is moving in a circle at a constant speed, and there are no external torques acting on the mass. Therefore, the angular momentum of the mass about the center of the circle remains constant.

This conservation principle is analogous to the conservation of linear momentum in linear motion. In a rotating system, if the radius of the circle changes, the velocity of the mass changes to conserve angular momentum. Conversely, if the velocity changes, the radius of the circle changes to maintain the angular momentum constant.

Therefore, in this scenario, the angular momentum of the mass about the center of the circle remains at $4 \, \text{kg m}^2/\text{s}^2$ as long as no external torques are acting on the system.