Question

A wheel of radius $1.5m$. is rotating at a constant angular acceleration of $10rad/s^2$. Its initial angular speed is $\left(\frac{60}{\pi }\right)$ rpm. what will be its angular speed and angular displacement at $t=2.0sec$?

Answer 1

Radius $r=1.5m,\alpha =10rad/s^2$

initial angular speed $w_0=\frac{60}{\pi }rpm=2\pi \times \frac{60}{\pi }\times \frac{1}{60}rad/s=2rad/s$

Time $t=2s$

From rotational kinematics

$w=w_0+\alpha t2+10\times 2=2+20=22rad/s$

and $\theta =w_{0}t+\frac{1}{2}\alpha t^2=2\times 2+\frac{1}{2}\times 10\times 4=4+20=24rad$