Question

An object is rotating about its center of mass. In space. The Boötes Void, to be less vague. Point A is on the surface of the object in the plane perpendicular to the axis of rotation.
Select all of the following properties that depend on the size and/or shape of the object.

a. Angular velocity of point A

b. Tangential acceleration of point A.

c.Tangential velocity of point A

d. Moment of inertia

e. Angular acceleration of point A

Can a normal force exert a non-zero torque on a sphere with respect to the center of mass?
Choose the correct answer with the correct explanation.

a. No, every direction perpendicular to the surface of a sphere goes through its center of mass.

b. No, torque can only happen from specific force types and the list does not include the normal force.

c. No, normal forces can only point up, which is directly towards the center of mass.

d. Yes, a normal force could point in a direction that is not pointing directly towards the center of mass.

e. Yes, any force can exert torque.

Thank you!

Answer 1

1. The moment of inertia depends on the size/shape of a object. The tangential velocity of point is equal to the angular velocity of the object times the distance of A from the axis of rotation.

The tangential acceleration depends on distance of the point A from the axis of rotation.

The angular acceleration is the rate of change of angular velocity, and they are independent of the shape of the object.

Hence, tangential acceleration of point A, tangential velocity of point A, and moment of inertia depend on the size/shape of the object.

2. No, every direction perpendicular to the surface of a sphere goes through its center of mass. Therefore the lever arm of the normal force is zero. Hence the torque is zero.