Question

A ballet dancer is rotating about his own vertical axis on smooth horizontal floor. The moment of inertia of the dancer decreases by 20% when he folds himself close to his axis of rotation. The % change in his rotational kinetic energy is:

• A. Increases by 36%
• B. Decreases by 36%
• C. Increases by 25%
• D. Decreases by 25%

Answer 1

The correct option is C Increases by 25%

Angular momentum is conserved.

$I_i=I$

$L=Iw$

$I_f=\left(0.8\right)I$

$KE=\frac{1}{2}I{w}^2=\frac{L^2}{2I}$

i.e. $KE\propto \frac{1}{I}$

If $I$ becomes $\frac{4}{5}$ then ,$KE$ will become $\frac{5}{4}.$

i.e. $KE$ will increase by $\underset{–}{25}$ %