Question

A circular disc of mass 10 kg and radius 0.2m is set into rotation about an axis passing through its centre and perpendicular to its plane by applying torque 10 Nm. Calculate angular velocity of the disc that it will attain at the end of 6 s from the rest.

Answer 1

Moment of inertia $I=\frac{m{r}^2}{2}=\frac{10\times {0.2}^2}{2}=0.2kg{m}^2$

Angular acceleration $\alpha =\frac{\tau }{I}=\frac{10}{0.2}=50rad/s^2$

Initial angular velocity $w_i=0$

Using $w_f=w_i+\alpha t$

Or $w_f=0+50\times 6=300rad/s$