Rotaional Inertia Cans Presenter: Tony Wayne, Albemarle High School
PH.5 The student will investigate and understand the interrelationships among mass, distance, force, and time through mathematical and experimental processes. Key concepts include
d) Newton’s laws of motion;
Newton;s 1st Law (Rotational Inertia)
Newton’s First Law of Motion. Specifically, rotational inertia. The idea is that the more rotational inertia an object has the harder it is to increase and decrease its rotational speed. Rotational speed is the time it takes to make one revolution.
Š Two identically sized cookie tins. It is good it they are different colors.
Š 20 steel washers about 1.75 inches in diameter
Š JB Weld epoxy
No safety issues with the demo. There are some safety issues with the epoxy used when making the demo.
Two sealed cookie tins are rolled down a gradual incline like a drag race. Switch the tins race lanes and the same can will win. Try a different angle for the incline and same tin wins. Ask the students why they think this would happen it they both have the same mass.
They answer is one can has more rotational inertia that the other. If you are so inclined you can open the two tins and expose the insides so the student scan see why one can does so much better. Explain that the can with the mass farther away from the center has more rotation inertia and is harder to speed up by rolling. This is good if coupled with other rotational inertia demos that illustrate the dependence on mass distribution.
How the physics is demonstrated
The rotational inertia of each tin is the sum of all its pieces. Because the two cans are identical, they will have the same rotational inertia. Call this Ican. Each can has 10 washers in it. These washers are concentrated in the center on one can and spread around the outside of the other can.
The can’s rotational inertia with the weights in the center is
Itotal =Ican + 10[1/2(mwasher)((Routside)2 – (Rinside)2))] where Routsde and Rinside refer to the outside and inside dimensions of the washer.
The other can’s washers are considered point masses. This can’s rotational inertia is
Itotal =Ican + 10[1/2(mwasher)R2] where, “R,“ is the distance to the inside edge of the can.
The masses of all ten washers is the same for each can. Since the distance to the inside of the can is larger than the diameter of the washers. (Conceptually, this is because there is more mass closer to the outside of the can.) The second can has the greater rotational inertia and is, therefore, harder to start rolling and more difficult to stop rolling.
Construction and Tips Regarding the Demonstration
Clean the cookie tins well. Scrub them with steel wool to roughen up the metal and give the epoxy a surface to cling to. Glue 10 or 12 washers together in a stack. Let dry overnight.
Epoxy the washers into the center of one of the cookie tins. Let dry overnight before handling it too much. Glue the other 10 or 12 washers to the inside rim of the remaining cookie tin. (Use the same number of washers in each cookie tin.) Space the remaining washers evenly around. Let dry. If the cookie tins are identical in color then mark one of the lids somehow so at a distance they look very different from each other. Mass the two cookie tins. Add a little clay to make then the same mass.
Have students mass the two cans. They are identical. Tilt the table up so that on end is about 3 inches higher than the other end. Have a drag race by rolling the two tins, side-by-side, down the table. Have students waiting at the bottom to catch the tins. If the cookie tins hit the floor, the washers will probably be knocked loose. Have a race with the two cans by rolling them side by side (The can with the washers on the edge will always lose.) Without opening the cans, have the students “feel” each can and then make a prediction as to why one can always loses. Next open the cans and discuss that the can with the washers on the edge has the same mass but more rotational inertia. It is harder to start rolling because of this extra rotational inertia.