A cylinder of mass 14.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 7.0 m/s. (a) Determine the translational kinetic energy of its center of mass. J (b) Determine the rotational kinetic energy about its center of mass. J (c) Determine its total energy.

(a) .

(b) .

(c) .

Explanation:

The translational kinetic energy of an object with mass and velocity is

.

In this question, and .

.

Let be the radius of this cylinder. Since this cylinder is rolling without slipping, its angular velocity would be .

The moment of inertia of a cylinder along its central axis is .

The rotational kinetic energy of that cylinder would be

.

Note that the radius of the cylinder, , can be eliminated from this expression.

.

The sum of the translational and rotational kinetic energy of this cylinder would be approximately .

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