A disc is rolling on the inclined plane. What is the ratio of its rotation KE to the total KE?

When a disc rolls down an inclined plane, it has two types of kinetic energy: translational and rotational. The translational kinetic energy is due to the movement of the center of mass of the disc along the incline, while the rotational kinetic energy is due to the disc spinning around its axis as it rolls.

For the solid disc, its moment of inertia plays an important role in determining how the energy is distributed between these two types of kinetic energy. For the disc that rolls without slipping, there exists a relationship between its linear velocity and its angular velocity, connecting the translational motion with the rotational motion.

When the total kinetic energy of the disc is analyzed, it is evident that the rotational kinetic energy is a part of the total energy. Once the contributions of both translational and rotational kinetic energy are evaluated, it is found that the ratio of the rotational kinetic energy to the total kinetic energy of a rolling disc is one to three. This means that for every part of kinetic energy contributed by rotation, three parts are from translation, thereby showing the balance between these two forms of energy in rolling motion.

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