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: Convert
\(600\) rpm \(=10\) rev/s \(=20\pi\) rad/s.

Step 2: Use the equation
It stops in \(30\) s, so \(0=20\pi-\alpha\times30\).

Step 3: Solve
\(\alpha=\frac{20\pi}{30}=\frac{2\pi}{3}\) rad/s\(^2\). Option (A).

Final Answer:
The retardation is \(\frac{2\pi}{3}\) rad/s\(^2\), option (A). \[ \boxed{\text{(A)}} \]