Question

A disc rotating about its axis from rest, acquires speed 500 rev/s in 4 seconds. The angle rotated by it during these four seconds (in radian) is

Answer 1

Answer:

angle rotated in 4 sec is 1000 radian

Answer 2

Answer:

The angle rotated by it during these four seconds is 2000π radian.

Explanation:

Given that,

Speed = 500 rev/s

Time = 4 sec

We need to calculate the angular acceleration

Using formula of angular acceleration

$\alpha=\dfrac{\omega_{f}-\omega_{i}}{t}$

Put the value into the formula

$\alpha=\dfrac{500\times2\pi}{4}$

$\alpha=250\pi\ rad/s$

We need to calculate the angle rotated by it during these four seconds

Using equation of motion

$\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2$

Put the value into the formula

$\theta=0+\dfrac{1}{2}\times250\pi\times16$

$\theta=2000\pi\ rad$

Hence, The angle rotated by it during these four seconds is 2000π radian.