Question

A wheel is rotating about an axis through its centre at $720rpm$. It is acted on by a constant torque opposing its motion for $8$ second 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

Answer: (B)

$72$

Initial frequency of rotation of wheel ${\nu }_i=720rpm=\frac{720}{60}=12rps$
So, initial speed of wheel $w_i=2\pi {\nu }_i=24\pi$ rad/s
Final speed of wheel $w_f=0$ rad/s
Time taken to stop $t=8s$
Angular acceleraion of wheel $\alpha =\frac{w_f-w_i}{t}=\frac{0-24\pi }{8}=-3\pi$ $rad/s^2$
So value of torque $\tau =I|\alpha |=\frac{24}{\pi }\times 3\pi =72Nm$