Question

part a

a constant net torque is applied to a rotating object. which of the following best describes the objects motion?

• the object will have a decreasing moment of inertia.
• the object will rotate with decreasing angular acceleration.
• the object will rotate with constant angular acceleration.
• the object will rotate with constant angular velocity.
• the object will have an increasing moment of inertia.
• the object will rotate with increasing angular acceleration.

Explanation:

Apply Newton's second law for rotation

$$ \tau_{\text{net}} = I \alpha $$

Analyze the relationship for constant net torque

$$ \tau_{\text{net}} = \text{constant}, \quad I = \text{constant} \implies \alpha = \frac{\tau_{\text{net}}}{I} = \text{constant} $$

Match with the correct option

$$ \alpha = \text{constant} \implies \text{The object will rotate with constant angular acceleration.} $$

Answer:

• The object will have a decreasing moment of inertia.
• The object will rotate with decreasing angular acceleration.
• The object will rotate with constant angular acceleration. (Correct answer)
• The object will rotate with constant angular velocity.
• The object will have an increasing moment of inertia.
• The object will rotate with increasing angular acceleration.