Question

a disc of mass m and radius r is rotating in a horizontal plane with angular velocity Omega and insect of mass m most from the centre to the circumference of the disc the new angular velocity of the disc

Answer 1

Given Data:

​Radius of disc, $=r$

Mass of disc, $=m$

Angular velocity of Disc, ${=w}_1$

New angular veloicity of disc after ant travel on it, $=w_2$

Step 1: Calculation of moment of inertia:

Applying conservation of angular momentum,

$I_1{w}_1=I_2{w}_2$

Moment of inertia of disc, $=\frac{1}{2}{MR}^2$

So,

$\frac{1}{2}M{R}^2{w}_1=(\frac{1}{2}M{R}^2+m{R}^2)w_2$

$M{R}^2{w}_1=(M{R}^2+2m{R}^2)w_2$

$w_2=\frac{M}{M+2m}\times w_1⟹w_2=\frac{M}{(M+2m)}{w}_1$