Ratio of Kinetic Energies for Rolling Sphere – Rankers Physics

Ratio of Kinetic Energies for Rolling Sphere

If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by: (1991)

$7 : 10$
$2 : 5$
$10 : 7$
$5 : 7$

Solution:

Translational kinetic energy is $E_t = \frac{1}{2}mv^2$ and rotational kinetic energy is $E_r = \frac{1}{2}I\omega^2 = \frac{1}{5}mv^2$. Total energy $E = \frac{7}{5}mv^2$, so the ratio $E_t / E = 5:7$.

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