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)

150

Answer 2

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 $= \frac{\theta}{2\pi}=\frac{300\pi}{2\pi}=150$