Question

A wheel having moment of inertia $4\, kg \,m ^{2}$ about its symmetrical axis, rotates at rate of $240\, rpm$ about it. The torque which can stop the rotation of the wheel in one minute is

• A. $\frac{5 \pi}{7} Nm$
• B. $\frac{8 \pi}{15} Nm$
• C. $\frac{2 \pi}{9} Nm$
• D. $\frac{3 \pi}{7} Nm$

Answer 1

Answer: (B)

$w=w_{0}-\alpha t$
$\alpha=\frac{w_{0}}{t}=\frac{2 \pi(240)}{60 \times 60}$
$\alpha=\frac{8 \pi}{60} rad / s ^{2}$
$\tau=l \alpha$
$=4 \frac{8 \pi}{60}=\frac{8 \pi}{15} N - m$