Question

A body is rotated about a fixed axis. Which of the following is correct about angular velocity?

• A. Angular velocity is constant for a rotating body.
• B. Angular velocity is proportional to the moment of inertia.
• C. Angular velocity depends on the angular acceleration.
• D. Angular velocity is independent of the axis of rotation.

Hint:

When analyzing rotational motion, remember that angular velocity and angular acceleration are closely related. If angular acceleration is constant, angular velocity will change linearly with time.

Answer 1

The Correct Option is C

Angular velocity (\(\omega\)) refers to how fast an object is rotating, and it is related to the angular displacement over time. The relationship between angular velocity and angular acceleration is given by: \[ \omega = \omega_0 + \alpha t \] Where: - \(\omega_0\) is the initial angular velocity, - \(\alpha\) is the angular acceleration, - \(t\) is the time. - (A) is incorrect because angular velocity is not necessarily constant. It can change depending on the angular acceleration. - (B) is incorrect because angular velocity is not proportional to the moment of inertia; it is related to angular acceleration, not the moment of inertia. - (D) is incorrect because angular velocity depends on the axis of rotation in cases of non-uniform rotation (for example, in non-central forces). Thus, the correct answer is that angular velocity depends on angular acceleration.