Question

A uniform circular platform of mass $120kg$ is rotating in horizontal plane about its own axis at the rate of $12rpm$ with a person of mass $40kg$ on the platform at its edge. If the person gently moves towards centre of platform where his moment of inertia becomes zero then, the angular velocity of platform is:

• A. $15rpm$
• B. $18rpm$
• C. $20rpm$
• D. $24rpm$

Answer 1

Answer: (C)

$20rpm$

Mass of the circular platform, $M=120kg$
Mass of the person, $m=40kg$
Initial Moment of Inertia, $I_1=\frac{M{R}^2}{2}+m{R}^2=\frac{120R^2}{2}+40R^2$

Final Moment of inertia, $I_2=\frac{M{R}^2}{2}=\frac{120R^2}{2}$

Using conservation of angular momentum as there is no external torque involved:
$I_1{N}_1=I_2{N}_2$

$\Rightarrow I_1\times 12=I_2{N}_2$ [As, $N2=12rpm$]

So, $N_2=20rpm$