Question

A flywheel at rest is set into rotation about an axis passing through its centre and perpendicular to its plane, to have an angular velocity of 24 rad/s in 6 second with constant angular acceleration. The total angle made by the flywheel during this interval is

• A. 24 rad
• B. 30 rad
• C. 48 rad
• D. 72 rad

Hint:

Find the angular acceleration first, then use the rotational equation of motion.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The flywheel starts from rest with constant angular acceleration, so \(\omega=\alpha t\) and \(\theta=\tfrac{1}{2}\alpha t^2\).

Step 2: Angular acceleration
\(\alpha=\dfrac{24}{6}=4\ \text{rad/s}^2\).

Step 3: Calculation
\(\theta=\tfrac{1}{2}\times 4\times 6^2=72\ \text{rad}\).

Final Answer:
The flywheel turns through 72 rad. \[ \boxed{\text{(D) }72\text{ rad}} \]