Downhill Race

Two cylinders that look the same may roll down a hill at different rates.

Two objects with the same shape and the same mass may behave differently when they roll down a hill. How quickly an object accelerates depends partly on how its mass is distributed. A cylinder with a heavy hub accelerates more quickly than a cylinder with a heavy rim.

Subjects:

Keywords:

motion

inertia

mass

kinetic energy

potential energy

rotation

exhibit-based

Tools and Materials

Two identical round metal cookie tins (such as those from butter cookies)
Ten large 1-inch zinc-plated steel washers (many sizes and types of washers will work, although a few large washers are more convenient than a lot of small ones; you just need the same number of washers in each tin and a reasonable amount of mass; heavy-duty refrigerator magnets may also work and will stick to the cookie tins)
Double-sided foam stick-on tape, masking tape, or adhesive-backed Velcro (use one or more of these as needed/convenient)
A ramp

Assembly

Arrange half of the washers evenly around the bottom of one tin, pushed up against the outside rim (click to enlarge photo).
Stack the remaining washers (equal in number to the first tin) in the middle of the bottom of the second tin (click to enlarge photo).
Secure the washers with tape or Velcro. (If you’re using magnets, they may stay in place without additional adjustment.)
Put the tops back on the tins.

To Do and Notice

Place both tins at the top of the ramp. Be sure the tops are on the tins. Ask your friends to predict which tin will reach the bottom of the ramp first. Release the tins and let them roll down the ramp. The tin with the mass closer to the center will always reach the bottom first.

What’s Going On?

At the top of the ramp, both tins have identical potential energy, since both have the same mass and are at the same height. At the bottom of the ramp, each tin will have part of its original potential energy appearing as linear (or translational) kinetic energy and the rest appearing as rotational kinetic energy.

Although both tins have the same total mass, each has this mass distributed differently. It’s harder to get the tin with distributed mass (washers pushed up against the outer rim) rotating compared with the tin that has its mass concentrated at the center. The tin with its mass at the rim will use more of its original potential energy just to get rolling. Therefore, it has less energy available to appear as translational kinetic energy, resulting in a lower linear speed. So, the tin with its mass concentrated around the rim will lose the race down the ramp, and the tin with its mass concentrated at the center will win.

Going Further

The use of lightweight “mag” wheels on cars is related to translational and rotational kinetic energy. Imagine that you had two cars of equal overall mass, but one had lightweight mag wheels and a heavy chassis, and the other had heavy steel wheels and a light chassis. Given the same energy input, the mag-wheel car would accelerate more rapidly, because less of the energy supplied would be needed to get the wheels rotating, and more would therefore appear as straight-line motion of the car as a whole.

It’s also interesting to experiment with rolling cans of soup down an inclined plane. Solid soups roll down the incline at a slower rate than liquid soups. The liquid does not have to rotate with the can, so the potential energy of the liquid soup can go into linear motion, not into rotation of the soup.