Question

A shaft initially rotating at $1725$ rpm is brought to rest uniformly in $20s.$ The number of revolutions that the shaft will make during this time is

• A. $1680$
• B. $575$
• C. $287$
• D. $627$

Answer 1

The correct option is C $287$

$0={\omega }_0-\alpha t$
$\therefore \alpha =\frac{{\omega }_0}{t}=\frac{\left(2\pi \right)\left(1725/60\right)}{20}$
$=9rad/s^2$
$\theta =\frac{1}{2}\alpha t^2=\frac{1}{2}\times 9\times (20{)}^2=1800rad$
$N=\frac{\theta }{2\pi }=286.4=287$