Introduction
Demonstrate how ice skaters rely on the conservation of angular momentum to attain their dramatic, highspeed rotation.
Materials
Dumbbells, 5lb, 2* Rotational platform, lowfriction *Materials included in kit.
Safety Precautions
When standing on a rotational turntable, or sitting on a rotating platform, stool or chair, maintain a low center of gravity over the center of the rotating apparatus in order to maintain optimal balance. Place the rotating platform in an open area away from objects, such as desks, chairs or walls. Maintain a controlled spin on the rotational platform. If the rotation is too fast, move arms away from the body to slow down the spin.
Procedure
 Place a lowfriction rotational platform in an area that is clear of objects, such as desks, chairs or walls. Ideally, the nearest objects should be several meters away in case of an accidental fall from the rotating platform.
 Recruit two student volunteers—one to be a “figure skater” and one to be a “rotator” who will slowly rotate the figure skater.
 Figure skater: Hold one dumbbell in each hand.
 Figure skater: Stand (or sit) in the center of the lowfriction rotational platform and maintain a low center of gravity over the center of the platform. If sitting on a rotational platform, pull legs in as close as possible to the center of the platform.
 Figure skater: Extend arms (and dumbbells) out to form a Tshape.
 Rotator: Slowly rotate the figure skater until a continuous rotational speed of approximately 30 revolutions per minute (one revolution every two seconds) is achieved.
 Rotator: Back away from the figure skater after a continuous rotation is reached.
 Figure skater: While maintaining a low center of gravity over the center of the platform, slowly pull arms and dumbbells towards the center of the body. Bring arms in tight. (Note: The rotational speed will increase considerably. If balance is lost, or rotation speed is uncomfortable, quickly extend arms to decrease speed or step off the rotational platform.)
 Observe the dramatic increase in rotational speed as the figure skater draws in his arms. What forces cause the figure skater’s rotation to increase?
 Repeat the demonstration several times with new volunteers.
 After the demonstrations, discuss the concepts of momentum and angular momentum with the class.
Teacher Tips
Student “figure skater” volunteers should be confident that they will be able to maintain proper balance on the rotating platform. Students who are susceptible to dizziness, or who might be uncomfortable when spinning should not perform this demonstration. Also, the figure skater must be able to support five pounds with each extended arm.
 The Rotational Turntable (Flinn Catalog No. AP4609) and Lab Stool Rotational Platform (Flinn Catalog No. AP6438) are excellent lowfriction rotational platforms for this demonstration that are available from Flinn Scientific, Inc. Rotating lab stools and rotating office chairs also work well for this demonstration. The rotating platform must spin smoothly and continuously for the most effective demonstration. Lubricate the axle bearings, if necessary, using grease or oil to minimize the amount of friction on the rotating axle.
 Additional angular momentum demonstrations that are available from Flinn Scientific include the Gyroscope Bicycle Wheel (Catalog No. AP4610), and the Ring and Discs (Catalog No. AP4634).
Answers to Questions
 Describe what happens when the rotating “figure skater” draws in his or her arms.
As the figure skater brings in his arms and the dumbbells close to his body, he begins to rotate very quickly—more than twice as fast as when his arms were extended outward. When he extends his arms again, his rotation slows down.
 What forces, if any, act on the “figure skater” once he or she is rotating? Does the “figure skater” apply a force on anything?
A small amount of friction acts against the rotating axle and causes the “figure skater” to slow down. There do not appear to be any external forces causing the rotation to increase. The “figure skater” applies a force to the dumbbells in order to move them towards and away from his body.
 Explain the observations (Questions 1 and 2) in terms of the conservation of angular momentum.
When the arms are in the extended position, the figure skater has a high moment of inertia. When the figure skater is rotated, he now has angular momentum. Since no forces act on the figure skater, his angular momentum is constant. As he draws in his arms, his moment of inertia decreases. Since his angular momentum must remain constant, he spins faster to compensate for the decrease in moment of inertia.
 How would the following scenarios affect the rate of rotation?
Same person holding 10lb dumbbells in each hand. The change in rotation rate would be the same if the individual held 10lb masses instead of 5lb masses because the starting and ending position of the masses are the same, so the relative moment of inertia change will be the same.
Different person of same mass, but with longer arms. The change in rotation rate would increase.
A tall person versus a short person of the same mass. The change in rotation rate would be the same.
A person whose mass is twice that of the original skater. The change in rotation rate would be smaller.
Discussion
In order to understand the conservation of angular momentum, several important physical properties must be discussed. To begin with, all objects have mass and, therefore, they have inertia. When an object is set in motion, the moving mass has a property known as momentum (or “inertia in motion”). As long as no external forces act on the object after it is set into motion, the momentum of the object will always be conserved—this is known as the law of conservation of momentum. The mass of an object that is rotating around an axis also has momentum, but it has a special type of momentum called angular momentum (or rotational momentum; “inertia of rotational motion”).
Angular momentum is slightly different from linear momentum because angular momentum depends not only on the mass of the object, but also on the distribution of the mass in relation to the rotational axis (axle). The value that describes an object’s mass and the mass distribution around an axis of rotation is known as an object’s moment of inertia (or rotational inertia). The moment of inertia of a rotating object is determined from the mass of the object multiplied by the square of the relative distance between the mass and the axis of rotation. The general form is I = Σmr^{2}, in which the moments of inertia of all the infinitely small masses that make up the object are determined from an axis of rotation, and then added together. Please refer to a physics textbook for further explanation. In general, when the average mass distribution is far from the axis of rotation, the moment of inertia of the object will be large. If the same amount of mass is located near the axis of rotation, the moment of inertia will be smaller. For example, imagine a hollow ring and a solid disc with the same mass and same diameter rolling down an inclined plane. The ring has all its mass distributed on the outside rim, far from the center of the ring (the axis of rotation). The disc’s mass is evenly distributed so the average distribution of mass will be closer to the center of the disk. Therefore, although the ring and disc have the same mass, their moments of inertia will be different. The disc will have a smaller moment of inertia compared to the ring.
The angular momentum of an object is equal to the moment of inertia multiplied by the rotational speed of the spinning object (Equation 1).
{12716_Discussion_Equation_1}
L = Angular momentum I = Moment of inertia of the spinning object ω = Rotational speed of the spinning object
Angular momentum is also always constant, as long as no external forces (such as friction) act on the rotating system. (When a force acts on a rotating system, the force acts at a distance from the axis of rotation through a lever arm and generates an “angular force” known as a torque.) In this demonstration, a spinning individual on a lowfriction rotational platform has constant angular momentum. When the "figure skater" draws in his arms, and the heavy dumbbells, close to the center of his body (his axis of rotation), his moment of inertia decreases. In order to maintain a constant angular momentum, his rotational speed must increase in accordance with the conservation of angular momentum. No external forces increase the speed of the “figure skater.” The internal force supplied by the figure skater to move the dumbbells closer to the body changes his moment of inertia, but does not affect his constant angular momentum. But, the internal force does result in an increase in the angular rotation.
This demonstration simulates the feat performed by figure skaters when they slowly spin with their arms extended. When the figure skater draws in his arms, his rotational speed increases dramatically.
