Question

A constant torque is acting on a wheel. If starting from rest, the wheel makes n rotations in t second, find the angular acceleration – 
1. \(\frac{{4\pi n}}{t}\;rad/\sec {\;^2}\)
2. \(\frac{{2\pi n}}{{{t^2}}}\;rad/\sec {\;^2}\)
3. \(\frac{{4\pi n}}{{{t^2}}}\;rad/\sec {\;^2}\)
4. None

Answer 1

Correct Answer - Option 3 : \(\frac{{4\pi n}}{{{t^2}}}\;rad/\sec {\;^2}\)

Initial angular velocity, ω₀ = 0

Number of rotations completed in t second = n

Angular displacement in t second, θ = 2πn

As \(\theta = {\omega _0}t + \frac{1}{2}\alpha {t^2}\)

\(\begin{array}{l} \Rightarrow 2\pi n = 0 + \frac{1}{2}\alpha {t^2}\\ \Rightarrow \alpha = \frac{{4\pi n}}{{{t^2}}}\;rad/\sec {\;^2} \end{array}\)