Question

A wheel is rotating at \(600\) rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in \(\text{rad}/\text{s}^2\) is (retardation is uniform)

• A. \(\frac{2π}{3}\)
• B. \(\frac{π}{4}\)
• C. \(π\)
• D. \(\frac{π}{6}\)

Hint:

Convert rpm to rad/s, then use $\omega=\omega_0-\alpha t$.

Answer 1

The Correct Option is A

Step 1: Use the average angular speed
Average speed $=\frac{20\pi}{2}=10\pi$ rad/s. Angle turned $=10\pi\times30=300\pi$ rad.
From $\omega_0^2=2\alpha\theta$: $400\pi^2=2\alpha\times300\pi$, so $\alpha=\frac{2\pi}{3}$.

Final Answer:
Option (A). \[ \boxed{\text{(A)}} \]