# A wheel is at rest. Its angular velocity increases uniformly and becomes 80 radians second after 5 seconds. the total angular displacement is:

Given,
$$\omega _{0}=0 (at rest)$$Angular velocity $$\omega$$= 80 rad/s
Time taken t = 5 sec
$$total displacement (0)=\omega _{0} t+\frac{1}{2}\alpha t^{2}$$$$\omega^{2} =\omega _{0}^{2} +{2}\alpha\theta$$$$\theta =\frac{\omega^{2}-\omega _{0}^{2}}{2\alpha }$$$$\alpha =\frac{\omega -\omega _{0}}{t}$$$$\alpha =\frac{80^{2}- (0)}{2*\frac{80-0}{5}}$$= 200 radian