Question

A disc rotating about its axis and starting from rest acquires an angular speed of 100 revolutions per second in 4 s. Find the angle rotated by it during this duration.

Answer 1

Given,

Initial angular speed = ${\omega }_i=0rad/s$

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

Time = $t=4\sec$

We know that,

Angular acceleration $\left(\alpha \right)=\frac{{\omega }_f-{\omega }_i}{t}$
$\alpha =\frac{100\times 2\pi -0}{4}=50\pi rad/s^2$
$t=4s$
$\therefore \theta =\frac{1}{2}\alpha t^2=\frac{1}{2}\left(50\pi \right)\times 4^2$
$\theta =400\pi radians$