Question

Two men of equal masses stand at opposite ends of the diameter of a turntable disc of a certain mass, moving with constant angular velocity. The two men make their way to the middle of the turntable at equal rates. In doing so

• A. Kinetic energy of rotation has increased while angular momentum remains the same
• B. Kinetic energy of rotation has decreased while angular momentum remains same
• C. Kinetic energy of rotation has decreased but angular momentum has increased
• D. both kinetic energy of rotation and angular momentum have decreased

Answer 1

The correct option is A Kinetic energy of rotation has increased while angular momentum remains the same

As there is no external torque, angular momentum is conserved
$I_1{\omega }_1=I_2{\omega }_2$
Since, men move towards middle of turn table $I_2$ decreases hence ${\omega }_2$ increases.
$\therefore \frac{{\omega }_2}{{\omega }_1}>1$
Now change in kinetic energy
$\therefore \Delta K=\frac{1}{2}{I}_1{\omega }_1^2-\frac{1}{2}{I}_2{\omega }_2^2$
$=\frac{1}{2}{I}_1{\omega }_1^2[1-\frac{I_2}{I_1}\frac{{\omega }_2^2}{{\omega }_1^2}]$
$\because \frac{{\omega }_2}{{\omega }_1}>1$
$=\frac{1}{2}{I}_1{\omega }_1^2[1-\frac{{\omega }_2}{{\omega }_1}]<0$
So kinetic energy increases.