Question

A wheel turning with angular speed of 30 rev/s is brought to rest with a constant acceleration. It turns 60 rev before it stops, the time that elapses before it stop, is

• A. 2s
• B. 4s
• C. 5s
• D. 6s

Answer 1

The Correct Option is B

$w=30\, rev / s , \theta=60\, rev$
$w_{f}^{2}=w_{1}^{2}-2 \alpha \theta$
$w_{f}=0$
$0^{2}=900\, rev / s ^{2}-2 \times \alpha \times 60\, rev$
$\alpha=\frac{900}{120} rev / s ^{2}$
$\alpha=75\, rev / s ^{2}$
$w_{f}=w_{i}-\alpha t \left(w_{f}=0, w_{i}=30\, rev / s , \alpha=7.5\right)$
$t=\frac{w_{i}-w_{f}}{\alpha}$
$t=\frac{30}{7.5} s$
$t=4\, s$