Question

A uniform disk rotating with constant angular acceleration covers $50$ revolutions in the first five seconds after the start. Calculate the angular acceleration and the angular velocity at the end of five seconds.

Answer 1

Here, it is given that ${\omega }_0=0$

Angular displacement of the wheel $=2\pi \times 50=100\pi radians$

Using the relation as

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

$100\pi =0+\frac{1}{2}\alpha {\left(5\right)}^2$

$\alpha =8\pi rad/{\sec }^2$

$\because 1revolution=2\pi rad$

$\alpha =4\pi rad/{\sec }^2$