Question

A uniform of mass $M=1kg$, radius $R=1m$ is moving towards right with velocity $v_s=20m/s$ and having angular velocity ${\omega }_0=4rad/s$ about the axis perpendicular to plane of the disc passing through centre of disc. Suddenly top point of the disc gets hinged about a fixed smooth axis. The angular velocity (in rad/s) of disk about new rotation axis is:

Answer 1

Given,

$M=1kgR=1m{v}_s=20m/s{\omega }_0=4rad/s$

Since MI of disc,

$I=\frac{1}{2}M{R}^2\therefore I=\frac{1}{2}Now,\tau =I\alpha \because \tau =I\omega \tau =I\omega \tau =\frac{1}{2}\times 4=2Nm\tau =I\alpha \alpha =\frac{2Nm}{1/2}rad/s{\omega }_2={\omega }_1+\alpha t=0+4\times \frac{1}{20}=0.2rad/s$