Rolling versus Sliding

Graphic - Two Aluminium Cylinders

Which is faster, rolling or sliding? Consider the two almost identical aluminum cylinders in the photograph above. One rolls without sliding, while the other slides without friction (to a good approximation) on four tiny ball bearings mounted at one end of the cylinder.

Suppose that they are started simultaneously from rest at the top end of an inclined plane, one rolling down the incline and the other sliding without friction, as shown in the photograph below.

Graphic - Inclined Plane

As they race down the incline, which one of the following will happen?

  1. The rolling cylinder will get to the bottom of the incline first.
  2. The sliding cylinder will get to the bottom of the incline first.
  3. They will get to the bottom at the same time; the race will end in a tie.

Solution

Reveal
Hide

Solution

The answer is (b); the sliding cylinder will get to the bottom first, as seen in this MPEG Video.

This behavior can be explained by consideration of conservation of energy. As either of the objects goes down the incline, its initial gravitational potential energy is converted into kinetic energy - energy of motion - so it gains speed.

In the case of the slider, because there is no frictional loss all of the initial potential energy is converted into linear kinetic energy. On the other hand, as the roller moves down the incline its potential energy is divide into two types of kinetic energy: translational (moving linearly) and rotational (circular motion). In the case of rolling, therefore, only part of the kinetic energy goes into linear motion, so the roller moves more slowly. In fact, the kinetic energy is divided between translational and rotational modes. Can you calculate this and determine how much faster the slider will go than the roller?