Question

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the centre of the disk. The platform has a mass of $150kg,$ a radius of $2.0m$, and a rotational inertia of $300kg{m}^2$ about the axis of rotation. A $60kg$ student walks slowly from the rim of the platform toward the center. If the angular speed of the system is $1.5rad/s$ when the student starts at the rim, what is the angular speed when she is $0.5m$ from the center?

• A. $1.2rad/s$
• B. $2.6rad/s$
• C. $3.6rad/s$
• D. $1.5rad/s$

Answer 1

The correct option is B $2.6rad/s$

Given: $m_{disc}=150kg,R=2m,I_{disc}=300kg{m}^2,$ $m_{student}=60kg,{\omega }_i=1.5rad/s,r=0.5m$
The initial rotational inertia of the system is

$I_i=I_{disk}+I_{student}$

Where $I_{disk}=300Kg{m}^{2}andR=2m$

The rotational inertia when the student reaches $r=0.5m$ is

$I_f=I_{disk}+m{r}^2$

Angular momentum conservation leads to

$I_i{\omega }_i=I_f{\omega }_f$

${\omega }_f=\frac{{\omega }_i(I_{disk}+m{R}^2)}{I_{disk}+m{r}^2}=\frac{1.5(300+60\times 2^2)}{300+60\times {0.5}^2}$

${\omega }_f=2.6rad/s$

FINAL ANSWER: (b)