Question

Under what conditions does a rigid body have angular momentum but not linear momentum?

1) when the translational velocity of the rotation is significantly greater than the translational velocity of the object's center of mass with respect to the chosen origin.
2) it is impossible for a rigid body to rotate such that it only has angular momentum without linear momentum.
3) when an object is rotating about a fixed axis but has no translational motion with respect to the chosen origin.
4) all rotating rigid bodies only have angular momentum with no linear momentum.

Answer 1

A rigid body has angular momentum but no linear momentum when it rotates about a fixed axis while its center of mass remains stationary with respect to the chosen origin.

Step-by-step explanation:

Under certain conditions, a rigid body can have angular momentum but not linear momentum. This situation occurs when the rigid body is rotating about a fixed axis but has no translational motion with respect to the chosen origin. Since all points on the rigid body move in circular paths about the axis of rotation, they have velocities that are tangent to the circles. This rotational movement provides the rigid body with angular momentum. However, if the center of mass of the rigid body is stationary with respect to the chosen origin, there is no linear momentum.

The answer to the student's question is: (3) when an object is rotating about a fixed axis but has no translational motion with respect to the chosen origin. For example, a spinning wheel that is mounted on an axle and not moving linearly has angular momentum due to its rotation but no linear momentum since its center of mass is stationary.