Question

A wheel rotation with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.

Answer 1

$\theta =100\pi ,\text{T}=5\text{sec}$

$\theta =\frac{1}{2}\alpha t^2$

$\Rightarrow 100\pi =\frac{1}{2}\alpha 25$

$\Rightarrow \alpha =8\pi \text{rad}/{\text{S}}^2$

$\omega ={\omega }_0+2t$

$=0+8\pi \times 5=40\pi \text{rad}/\text{s}$

$=20\text{rev/s}$