Question 518: Centre of Mass and Rotational Motion

Question

If the angular velocity of a body rotating about the given axis increases by $20 \%$, then its kinetic energy of rotation will increase by

Accepted Answer

$$\begin{aligned}
& \omega_2=\frac{120}{100} \omega_1=1.2 \omega_1 \
& \frac{K E_2}{K E_1}=\frac{\frac{1}{2} \mathrm{I} \omega_2^2}{\frac{1}{2} \mathrm{I} \omega_1^2}=\frac{\omega_2^2}{\omega_1^2}=\frac{\left(1.2 \omega_1ight)^2}{\omega_1^2}=1.44 \
& 	herefore \quad \mathrm{KE}_2=1.44 \mathrm{KE}_1 \
& 	herefore \quad\left(\frac{\mathrm{KE}_2-\mathrm{KE}_1}{\mathrm{KE}_1}ight) 	imes 100=\left(\frac{1.44 \mathrm{KE}_1-\mathrm{KE}_1}{\mathrm{KE}_1}ight) 	imes 100 \
& =0.44 	imes 100=44 \%
\end{aligned}$$

Answer

$20 \%$

Answer

$30 \%$

Answer

$44 \%$

Answer

$66 \%$

Centre of Mass and Rotational Motion

If the angular velocity of a body rotating about the given axis increases by 20 \%, then its kinetic energy of rotation will increase by

Choose the correct answer: