Question

A flywheel of moment of inertia $9 \times 10^{3} kg m ^{2}$ is rotating with uniform angular speed of $5 rad s ^{-1}$ If a torque of $9 \times 10^{4}$ Nm retard the wheel, then time in which the wheel comes to rest is

• A. $25 \,sec$
• B. $30 \,sec$
• C. $50 \,sec$
• D. $60 \,sec$

Answer 1

Answer: (C)

As we know that, $\omega=\omega_{0}+\alpha t$
$\therefore \frac{\omega-\omega_{0}}{t}=\alpha$
$\Rightarrow \alpha=\frac{0-5}{t}=\frac{-5}{t} rad\,s^{-2}$
$\therefore \tau=I \alpha$
$\Rightarrow 9 \times 10^{4}=9 \times 10^{3} \times \frac{5}{t}$
$\Rightarrow t=50\, sec$