The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is
The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is
disc
sphere
cylinder
ring
Solution
Translational kinetic energy of a ring is:
$\mathrm{KE}_{\text {Trans }}=\frac{1}{2} \mathrm{mv}^2$
Rotational kinetic energy of the ring is:
$\begin{aligned}
\mathrm{KE}_{\text {Rolling }} & =\frac{1}{2} \mathrm{I} \omega^2 \\
& =\frac{1}{2} \mathrm{mR}^2 \omega^2 \\
\mathrm{KE}_{\text {Rolling }} & =\frac{1}{2} \mathrm{mv}^2 \quad(\because \mathrm{v}=\omega \mathrm{R})
\end{aligned}$