Question

A flywheel rotating at 420 rpm slows at a constant rate of 2 rad $s^{-2}$. Find the time required to stop the flywheel.

• A. $22s$
• B. $11s$
• C. $44s$
• D. $12s$

Answer 1

The correct option is A $22s$

Initial angular speed, ${\omega }_0=420$ $rpm=\frac{420}{60}=7$ $rps=7\times 2\pi =14\pi$ $rad/s$

Final angular speed, $\omega =0$ $rad/s$

Acceleration, $\alpha =-2$ $rad/s^2$ (negative sign because flywheel is deccelerating)

From kinematics:

$\omega ={\omega }_0+\alpha t$

$⟹t=\frac{\omega -{\omega }_0}{\alpha }$

$⟹t=\frac{-14\pi }{-2}$

$⟹t=7\pi$

$⟹t=22$ $s$