A man of 80 kg is standing on the rim of a circular platform of mass 200kg. The platform rotates about its axis at 12 r.p.m. The man moves from rim to centre of the platform. How will the system rotate?(The moment of inertia of man at the centre may be neglected)

If r is the radius of the platform and M its mass, Moment of inertia of platform about the axis  $=\frac{{\mathrm{Mr}}^2}{2}.$

Moment of inertia of the system with the man at  the rim $=\frac{{\mathrm{Mr}}^2}{2}+{\mathrm{mr}}^2$

$=\frac{200r^2}{2}+80r^2=180r^2$

Moment of inertia with the man at the centre is  $\frac{{\mathrm{Mr}}^2}{2}=100{\mathrm{r}}^2$

By conservation of angular momentum,  $180{\mathrm{r}}^2{\omega }_1=100{\mathrm{r}}^2{\omega }_2$

${\omega }_2=\frac{180}{100}{\omega }_1=\frac{180\times 12}{100}=21.6\mathrm{rpm}$