Question

A wheel is at rest.Its angular velocity increases uniformly and becomes 80 radian per second after 5 s.The total angular displacement is:

Answer 1

From kinematics laws :

$\omega ={\omega }_0+\alpha t$ ..(1)

$\theta ={\theta }_0+{\omega }_{0}t+\frac{1}{2}\alpha t^2$....(2) where,

$\omega$ is final angular velocity

${\omega }_0$ is initial angular velocity

$\theta$ is angular displacement

$\alpha$ is angular acceleration and $t$ is time

From (1), $80=0+5\alpha$

$\alpha =16rad/s^2$

From(2), $\theta =0+0+\frac{1}{2}\times 16\times 25=8\times 25=200rad$