Question

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.

Answer 1

Given that,${\omega }_0=0$

$\omega =100\text{rev}/\text{s}$

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

$\therefore \alpha =\frac{\omega }{t}$

$\alpha =\frac{100}{4}\text{rev}/{\text{S}}^2=25\text{rev}/{\text{S}}^2$

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$=\frac{1}{2}\times 25\times 16$

$=200\text{degree}$

$=200\times 2\pi \text{radians}$

$=400\pi \text{radians}$