Question

A woman of mass m stands at the edge of a solid cylindrical platform of mass $M$ and radius $R$. At $t=0$ the platform is rotating with negligible friction at angular velocity ${\omega }_0$ about a vertical axis passing through the centre. The woman begins to walk with speed v, relative to the platform, towards the center of the platform.

• A. Angular velocity when woman reaches the centre is $(v+\frac{m}{M}){\omega }_0$
• B. Angular velocity as function of time is $\omega =\frac{M+m}{M+2m(1-vt/R{)}^2}$
• C. Energy of system is conserved
• D. Momentum of woman increases in magnitude

Answer 1

The correct option is C Energy of system is conserved

As the woman start moving towards the center of the platform the center of the mass of the whole system move towards the center of platform.

Hence, moment of inertia decreases as no external torque is being applied

the total angular momentum remains constant.

This results in increase of angular velocity.

Energy $=1/2I{\omega }^2$

Here I decreases and omega increases.

So, energy remains constant,