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:

The initial angular speed of the wheel is ${\omega }_0=0$

The final angular speed of the wheel is ${\omega }_f=100rev/s$

${\omega }_f=100rev/s\times 2\pi =200\pi rad/s$

Using the equation of motion for the wheel:
$\Rightarrow {\omega }_f={\omega }_0+\alpha t$
$\Rightarrow {\omega }_f=\alpha t$

$\Rightarrow \alpha =\frac{200\pi }{4}=50\pi rad/s^2$ or $25rev/s^2$

Now, the angular displacement of the wheel is given as:

$\therefore \theta ={\omega }_t+\frac{1}{2}\alpha t^2$

$\theta =0+\frac{1}{2}\times 50\pi \times (4{)}^2=400\pi rad$

$\therefore \alpha =50\pi rad/s^2$ or $25rev/s^2$

$\theta =400\pi rad$.