Question

A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad\, s^{-1}$ to $40\pi \, rad\, s^{-1}$ in 10 seconds. How many rotations did it make in this period?

• A. 80
• B. 100
• C. 120
• D. 150

Answer 1

Answer: (D)

As $\omega_{2}=\omega_{1} +\alpha t \:\:\: \therefore \: 40\pi + 20\pi + \alpha \times10 $ or $ \alpha = 2\pi \, rad \, s^{-2}$
From, $\omega_{2}^{2} -\omega_{1}^{2} = 2 \alpha \theta $
$ \left(40\pi\right)^{2} -\left(20\pi\right)^{2} =2 \times2\pi\theta $
or $\theta = \frac{1200\pi^{2}}{4\pi} =300\pi$
No. of rotations completed $= \frac{\theta}{2\pi}=\frac{300\pi}{2\pi}=150$