Rotaional Inertia Cans Presenter: Tony Wayne, Albemarle High School

Va. SOL:

PH.5 The student will investigate and
understand the interrelationships among mass, distance, force, and time through
mathematical and experimental processes. Key concepts include

É

d)
NewtonÕs
laws of motion;

National Standards:

Newton;s 1^{st} Law (Rotational Inertia)

Topic/Concept

NewtonÕs 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.

Materials

á Two identically sized cookie tins. It is good it they
are different colors.

á 20 steel washers about 1.75 inches in diameter

á JB Weld epoxy

Safety Considerations

No safety issues with the demo. There are some safety
issues with the epoxy used when making the demo.

Presentation

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 I_{can}. 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 canÕs rotational inertia with the weights in the center is

I_{total} =I_{can} + 10[1/2(m_{washer})((R_{outside})^{2}
– (R_{inside})^{2}))] where R_{outsde} and R_{inside}
refer to the outside and inside dimensions of the washer.

The other canÕs washers are considered point masses. This canÕs rotational inertia is

I_{total}
=I_{can} + 10[1/2(m_{washer})R^{2}] where, ÒR,Ò 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 ÒfeelÓ 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.