Question

A ballet dancer is rotating about his own vertical axis. Without external torque if his angular velocity is doubled then his rotational kinetic energy is:

• A. halved
• B. doubled
• C. quadrupled
• D. unchanged

Answer 1

Answer: (B)

doubled

No external Torque,
$\therefore$ Angular momentum will remain constant.
${\omega }_1=\omega$
${\omega }_2=2\omega$
$I_1{\omega }_1=I_2{\omega }_2$
$I_2=\frac{I}{2}$
Rotational ${KE}_1=\frac{1}{2}I{\omega }^2$
${KE}_2=\frac{1}{2}\times \left(\frac{I}{2}\right)(2\omega {)}^2$
$=\frac{1}{2}\times 2{\omega }^2$

$\frac{{KE}_2}{{KE}_1}=\frac{2}{1}$