A wheel is rotating at 480 rpm. Find the magnitude of angular acceleration required to stop the wheel in 8 s.

A wheel is rotating at 480 rpm. Find the magnitude of angular acceleration required to stop the wheel in 8 s.
  1. $2 \pi \mathrm{rad} \mathrm{s}^{-2}$
  2. $2.5 \pi \mathrm{rad} \mathrm{s}^{-2}$
  3. $2 \mathrm{rad} \mathrm{s}^{-2}$
  4. $3.5 \mathrm{rad} \mathrm{s}^{-2}$

Solution

Given, initial angular speed, $\omega_i=480 \mathrm{rpm}$ $=\frac{480}{60}=8 \mathrm{rps}=8 \times 2 \pi=16 \pi \mathrm{rad} \mathrm{s}^{-1}$ Time, t = 8s Final angular speed, $\omega_f=0$ From first equation of motion, $ \begin{array}{rlrl} \omega_f & =\omega_i+\alpha t \\ \Rightarrow & \frac{\omega_f-\omega_i}{t} & =\alpha \Rightarrow \alpha=\frac{0-16 \pi}{8} \\ \therefore & \alpha & =-2 \pi \mathrm{rad} \mathrm{s}^{-2} \end{array} $ Therefore, magnitude of angular acceleration, $ |\alpha|=2 \pi \mathrm{rads}^{-2} $

Asked in: AP EAMCET 2021 (25 Aug Shift 2)

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