Question

A wheel having moment of inertia $2kg{m}^2$ about its axis, rotates at 50 rpm about this axis. What is the torque that can stop the wheel in one minute?

• A. $\frac{2\pi }{18}Nm$
• B. $\frac{\pi }{8}Nm$
• C. $\frac{\pi }{12}Nm$
• D. $\frac{\pi }{18}Nm$

Answer 1

The correct option is D $\frac{\pi }{18}Nm$

${\omega }_0=50rpm=\frac{100\pi }{60}rad/s=\frac{5\pi }{6}\alpha =\frac{Z}{I}{\omega }^{\prime }={\omega }_0-\alpha t=\frac{5\pi }{3}-\frac{Z}{I}tt=60sec,{\omega }^{\prime }=0\therefore \frac{5\pi }{3}-\frac{Z}{2}60=0\Rightarrow \frac{5\pi }{3}=30Z\Rightarrow Z=\frac{\pi }{18}Nm$