Question

A circular platform is mounted on a vertical frictionless axle. Its radius is $r=2m$ and its moment inertia is $I=200kg$ $m^2$. It is initially at rest. A $70kg$ man stands on the edge of the platform and begins to walk along the edge at speed $v_0=10{ms}^{-1}$ relative to the ground. The angular velocity of the platform is

• A. $1.2rad$ $s^{-1}$
• B. $0.4rad$ $s^{-1}$
• C. $2.0rad$ $s^{-1}$
• D. $7.0rad$ $s^{-1}$

Answer 1

The correct option is D $7.0rad$ $s^{-1}$

As there is no external torque, thus $L$ is conserved.

Let angular velocity of the platform be $w.$

$L_i=L_f$

$0=Iw-m{v}_{o}r$

$0=200\left(w\right)-70\left(10\right)\left(2\right)$

$⟹w=7rad/s$