Q.23 A flywheel of a motor has mass 100 kg and radius 1.5 m. The motor develops a constant torque of 2000 Nm. The flywheel starts rotating from rest. Calculate the work done during the first 4 revolutions.
Best answer
Answer: \(W = 16000\pi \approx 5.027 \times 10^4\) J
For a constant torque, work done \(W = \tau\theta\). In 4 revolutions, \(\theta = 4 \times 2\pi = 8\pi\) rad.
\[W = 2000 \times 8\pi = 16000\pi = 16000 \times 3.142 = 50272 \text{ J} \approx 5.03 \times 10^4 \text{ J}\](The mass and radius are not needed for the work. They would give the moment of inertia, e.g. \(I = \frac{1}{2}MR^2 = 112.5\) kg m\(^2\) for a disc, which equals the kinetic energy gained \(\frac{1}{2}I\omega^2 = W\), from which the final angular speed could be found.)
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