A rolling sphere without slipping will have the motion of both translational and rotational motion, which are as follows: center of mass, and the rolling around its axis. The kinetic energy of a sphere is found to be both translational as well as rotational. Translational motion depends on its linear velocity while rotational motion is dependent on the angular velocity of the sphere.

The ratio of translational kinetic energy to the total kinetic energy for a rolling sphere is always 10:7. This particular ratio is due to the unique distribution of the sphere’s mass and geometry. A portion of the total energy is dedicated to the translational motion of the center of mass, while the remaining energy contributes to the rotational motion.

Generally, the translational energy is much higher than the rotational energy because the moment of inertia of a sphere is lower compared to the other shapes; hence, the sphere requires much less energy for it to rotate. This way, the rolling motion of the sphere is preserved without slipping.

This ratio is an important concept in physics because it demonstrates the connection between different energies involved in rolling motion. This is particularly helpful in solving problems dealing with energy conservation and dynamics in rolling objects across different surfaces.

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