Question

A wheel rotating with uniform angular acceleration covers $50$ rev in the first five seconds after the start. If the angular acceleration at the end of five seconds is $x\pi rad/s^2$, find the value of $x$.

Answer 1

$\theta =\frac{1}{2}\alpha t^2$
$\therefore \alpha =\frac{2\theta }{t^2}=\frac{2\left(50\right)\left(2\pi \right)}{(5{)}^2}$
$=\left(8\pi \right)rad/s^2$
$=25.14rad/s^2$
Comparing with given $\alpha$, $x=8rad/s^2$