Question

A wheel is rotating about an axis through its center at 720 rpm. It is acted on by a constant torque opposing its motion for 8 seconds to bring it to rest finally. The value of torque in Nm is (given I=$\frac{24}{\pi }kg-m^2$)

• A. 48
• B. 72
• C. 96
• D. 120

Answer 1

The correct option is B 72

Initial frequency of rotation of wheel $f_i=720rpm=\frac{720}{60}=12rps$

Initial angular velocity $w_i=2\pi f=2\pi \times 12=24\pi$

Final angular velocity $w_f=0$

Time $t=8s$

Using $w_f=w_i-\alpha t$

or $0=24\pi -\alpha \times 8$ $⟹\alpha =3\pi$

Torque $\tau =I\alpha =\frac{24}{\pi }\times 3\pi =72Nm$