Time taken by man to complete one revolution on platform – Rankers Physics

Time taken by man to complete one revolution on platform

A circular platform is mounted on a frictionless vertical axle. Its radius $R = 2\text{ m}$ and its moment of inertia about the axle is $200\text{ kg m}^{2}$. It is initially at rest. A $50\text{ kg}$ man stands on the edge of the platform and begins to walk along the edge at the speed of $1\text{ ms}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is: (2012 Mains)

$\pi\text{ s}$
$3\pi/2\text{ s}$
$2\pi\text{ s}$
$\pi/2\text{ s}$

Solution:

Angular velocity of man $\omega_{m} = \frac{v}{R} = 0.5\text{ rad/s}$. By conservation of angular momentum, $I_{p}\omega_{p} + I_{m}\omega_{m} = 0$, giving $\omega_{p} = -0.5\text{ rad/s}$. Relative angular velocity $\omega_{rel} = \omega_{m} - \omega_{p} = 1\text{ rad/s}$. Time $T = \frac{2\pi}{\omega_{rel}} = 2\pi\text{ s}$.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Questions

Explore conceptually related problems

1. If the ice on the polar caps of the Earth melts, the duration of day will
2. A particle of mass \(m\) is moving on a circle of radius \(R\) with kinetic energy \(K\). Then angular momentum of particle about centre of circle will be:
3. Assertion (A): A cyclist always bends inwards while negotiating a curve Reason (R): By bending he lowers his centre of gravity  
4. Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation (2018)
5. Assertion (A): If there is no external torque on a body about its centre of mass, then the velocity of the center of mass remains constant. Reason (R): The angular momentum of a system always remains constant.