Asolid cylinder rolls without slipping along a horizontal surface, at constant speed v. calculate the fraction of the total kinetic energy of the cylinder that arises from rotational motion.

The rotational kinetic energy is 1/3 of the total kinetic energy of the cylinder.

Explanation:

Since the kinetic energy of the cylinder will be composed of 2 parts

1) Kinetic energy due to translational motion.

2) Kinetic energy due to rotational motion of the cylinder.

Thus the total kinetic energy of the cylinder equals

We know that for solid cylinder the moment of Inertia (I) is given by

Thus applying values we have

Now in rolling we know that

Applying values in the ration above we obtain

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