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Published: 18 December 2020

• mechanics
• simulation

This week we’re taking a look at a deceptively simple demonstration, D1-61: Rolling versus Sliding. An aluminum cylinder rolls down an inclined plane. An identical aluminum cylinder has tiny bearings on one end, so that when stood upright on that end it effectively slides almost without friction down the incline. You might invite your students to make a prediction: If the two cylinders are started from the top at the same time, will the rolling cylinder or the sliding cylinder reach the bottom of the incline first?

The two cylinders start at the same height with the same potential energy. As they slide or roll down the ramp, that potential energy is converted into kinetic energy. Linear kinetic energy is proportional to the mass of the cylinder and the square of its velocity. However, the rolling one also has rotational kinetic energy, which is proportional to the moment of inertia of the cylinder and the square of its angular velocity. So for the rolling cylinder, some of the potential energy is converted into rotational kinetic energy as it rolls, and only some of the potential energy is converted into linear potential energy, giving it a lower velocity as it goes down the ramp.

So the sliding cylinder reaches the bottom first!

It can be helpful to illustrate this exchange of energies with graphs. Andrew Duffy at Boston University has created simulations with animated energy graphs, one here for a mass sliding down a ramp, and another here for a mass rolling down a ramp. Try them out for yourself! You can see that the potential and kinetic components always sum to the same total energy, showing that energy is conserved.