Question

A wheel having moment of inertia $2{\text{kgm}}^2$ about its axis, rotates at $50\text{rpm}$ about this axis. Find the torque$\text{(Nm)}$ that can stop the wheel in one minute.

• A. $\frac{\pi }{9}$
• B. $\frac{\pi }{18}$
• C. $-\frac{\pi }{9}$
• D. $-\frac{\pi }{18}$

Answer 1

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

Given, $I=2kg-m^2{\omega }_0=50rpm=50\times \frac{2\pi }{60}=\frac{5\pi }{3}rad/s\omega =0t=1min=60sec$

Using kinamatics equation= $\omega ={\omega }_0+\alpha t$
$0=\frac{5\pi }{3}+\alpha \times 60\alpha =-\frac{\pi }{36}red/s^2$
(here negative sign shows the deceleration )

$\tau =I\alpha =2\times (-\frac{\pi }{36})=-\frac{\pi }{18}$visualise