Demonstration Information

	Title:	A Day at the Races - Moment of Inertia
	Course Area:	Dynamics
	Authors:	Al Estes, Charlie Packard and Tom Messervey

Bottom Line Up Front:

This is a demonstration of the basic principles underlying the behavior of rotating bodies. A race between two different cylinders on a ramp is used to show that the closer the mass of an object is concentrated to an axis of rotation, the faster it will spin because it has a lower moment of inertia, which is a measure of a body’s resistance to rotation.

Principle: The mass moment of inertia (Vector Mechanics for Engineers—Dynamics by Beer, Johnston and Clausen, 8th Ed, pg. 1296) is a rigid body’s resistance to rotation and is a measure of the distribution of mass of a rigid body relative to a given axis of rotation. In its most general form, the mass moment of inertia is given by the equation below. For a solid cylinder and a hollow cylinder, the equations for the mass moment of inertia about the axis of interest in our demonstration reduce to those in the figure below (or see http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi). In the figure, “M” represents the mass of the rigid body and “R” represents the radius of the solid cylinder, and “a” and “b” represent the inner and outer radii of the hollow cylinder.

Support Formula(s):

Click to enlarge

What You Will Need:

Item Name:

Quantity:

Description:

Inclined Plane

1

An inclined plane able to support both rolling cylinders simultaneously

“Steel Wheel”

1

A steel cylinder of approximately 3” length and 1” diameter with a wooden core. The cylinder weight is approximately the same as “Rolling Timber” (may be available through Arbor Scientific)

“Rolling Timber”

1

A wooden cylinder of approximately 3” length and 1” diameter with a steel core. The cylinder weight is approximately the same as “Steel Wheel” (may be available through Arbor Scientific)

12” Ruler

1

Used to start the race

How It's Done:

Before Class


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Measure and calculate the basic parameters (mass, diameters) and practice the demonstration. Make sure the release is clean and that the demonstration can be seen clearly from all locations in the classroom. If the classroom is very large, consider making larger cylinders and ramps than those shown here.

In Class

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The video included in the “Little bit extra” section provides a brief synopsis of the demonstration. First establish the scenario by introducing and describing “the players” in your best race announcer’s voice. Then, without any analysis, ask the students to guess which “player” will win the competition. Ensure you record this on the board. Build up to the start of the race and stop just short of letting them go. Ask students to consider if weight might be a factor affecting the outcome, then provided the class with the weight of each player and see if their guesses change (record on the board). Again, build up to the start and stop short to discuss the concept of mass being a resistance to translation and moment of inertia as resistance to rotation. Have students help you calculate the moment of inertia for each of the players (figure 4) and take a final tally of the bets. Finally, let the race happen!

Observations

Given that the overall dimensions and the weight of the cylinders are approximately the same, the student should observe that the outcome depends on the moment of inertia and not the weight.

That Little Bit Extra:

Download additional files:

Hype up the event by dramatizing the race! Consider using racetrack videos and noises which can easily be found on the internet. Ask students to guess which will win once the scenario is set up and before the principles are discussed. Build suspense by working your way to the “gun shot” starting the race, then backing off the start to analyze another aspect. If you’re using Power Point, incrementally build your slides to build suspense! Furthermore, cylinders of different materials and diameters might be considered (see photo).