Hands-on Science Carnival 2010 Activity Stations: General Physics

Spinning Things: Angular Momentum and Gyroscopic Motion

[Shopping List: GyroWheels; rotating platforms; water bottles and dumbbells; bicycle wheel; rope; store-bought and home-made X-Zylo flying rings with launcher; boomerangs; frisbies; Flip-n-Flyer]

Conservation of Angular Momentum

1. Have kid sit cross-legged on a rotating platform.
2. Have them hold a dumbbell (or water bottle) in each hand, with both arms fully extended to their sides.
3. Gently spin them while they hold their arms straight out, then step away and ask them to bring both arms slowly into their chest. They will rotate much faster. Be sure they move both arms together or they will become unbalanced and may fall off.
4. To slow their rotation ask them to slowly spread their arms back out again. They can control their rotation speed by their arm position.

What's Happening: An object in motion has momentum, which is the product of the object's mass times it's velocity (speed and direction), and unless acted upon by an external force, this momentum remains constant. We call this the Law of Conservation of Momentum, and this means that as long as the mass doesn't change, neither does the velocity of the object. Nothing ever changes, which makes for pretty boring motion, that is until we introduce rotation to the system. For rotating objects we have angular momentum, which is also conserved as long as no external force acts on the object. But angular momentum depends not only on the angular velocity (rotations per time unit about a particular axis direction) and the mass, but also on where the mass is located. Thus by changing the location (or distribution) of the objects mass, we can change the angular velocity of the object- dramatically! For a constant amount of momentum, a mass nearer the axis will rotate faster than the same mass moved farther from the axis. An ice skater takes advantage of this- she starts spinning slowly on one skate with her arms and her other leg far from her body, then brings her arms and leg in very close to her body- and thus the axis about which she is spinning- and increases her angular velocity- how fast she spins- a lot! To slow down or stop, she simply extends her arms and leg again.

Gyroscopic Motion- the GyroWheel

[Note: please be very careful not to drop the GyroWheel on its handle or you will damage the internal bearings]

1. Again have kid sit cross-legged on a rotating platform.
2. Notice that the left and right sides of the GyroWheel are labeled. Start up the internal flywheel with its motor by pressing the button on the left side. One press gives the slowest speed, two presses medium speed, and three presses gives the fastest speed (and most effect in the demo.) Once you pause 2 or 3 seconds, another push will turn the motor off.
3. You will immediately feel the gyroscopic forces, and while the flywheel is accelerating to constant (angular) speed the entire wheel and tire may spin, but it is easy to stop. Once the flywheel reaches its constant speed, the wheel should remain stationary.
4. Hand the wheel to the kid on the platform. It may be harder than you expect!
5. Because the wheel is not turning, the kid may hold it any way they like, or even set it in his lap or on the platform if it's too heavy for them.
6. As he tips and turns the wheel he will begin to rotate on the platform.

What’s Happening: Gyroscopic motion is much too complicated to fully explain here. Perhaps the best way to begin to understand what is happening is to think about a hockey puck sliding across the ice. It will continue moving in a straight line forward until you gently tap it on its right side, but it doesn't then move directly to the left as you might expect; instead its new direction of motion is a combination of the forward velocity it had originally plus the new velocity you gave it toward the left, producing motion at an angle forward and to the left. Just as the hockey puck will continue to move in a straight line until you apply an external force, the spinning flywheel inside the GyroWheel will continue to spin with its axis pointing in the same direction until you apply an external force. It's just a big gyroscope, but because we don't tend to think of spinning quite the same as we do linear motion, the resulting motion when we apply an external force to a spinning object is quite surprising and non-intuitive. This is what you feel as you hold the GyroWheel and try to move it in various directions. Finally, because the angular momentum of a system, in this case the kid on the platform holding the wheel, must remain constant as long as no external force is applied, changing the angular momentum of the spinning wheel (by changing the direction its axis points, i.e. tipping or turning it), results in a change to a different axis of rotation, in this case the axis of the rotating platform, in order to keep the total angular momentum (the sum) unchanged. For example, if the kid is holding the wheel upright (as if it were mounted to a bicycle) with the flywheel spinning forward (i.e. like a bicycle rolling forward), then tipping the top of the wheel to the right (as though the bike is falling to the right) will make the platform (and kid) rotate to the right or clockwise. Tipping it to the left wil make him rotate left or counter-clockwise. The faster he tips the wheel, the faster he rotates.

If you are not standing or sitting on a rotating platform as you tip the wheel, then the wheel itself will turn in the direction you tip it- try it. This is called gyroscopic precession, and is what actually allows us to easily balance a two wheeled bicycle. As we roll forward and begin to fall or tip to the right, the front wheel turns to the right and the bicycle begins to ride in a clockwise circle to the right. Now recall what happens when you are riding in a car which turns rapidly to the right, centrifugal force (or really the lack of a centripetal force on you) throws you towards the left side of the car. Back to the bicycle, friction holds the wheel to the road, so as you begin to turn to the right centrifugal force acts on those parts of the bike- and you- that aren't stuck to the road and straightens the bike up, which straightens the wheel, and off you go until you start to tip over a little again and the whole process repeats. The faster you ride (and/or the heavier your wheel), the more pronouced all of these forces are, and thus the easier it is to balance the bicycle. That's why it's so difficult for a child to learn to ride a bike- he simply isn't moving fast enough to benefit from this gyroscopic stabilizing effect. And that is what the GyroWheel is really intended to do- create the effect of a heavy wheel spinning very fast (the internal flywheel) even though the tire is rotating very slowly (terrified little kid speed!) The GyroWheel is a hi-tech replacement for old-fashioned training wheels invented by college engineering students. It's also a significant improvement, because training wheels actually teach kids the wrong way to react when they begin to tip over (think about it.)

Variations: Play around with the GyroWheel. Set it on the ground and try to tip it over-really! See what happens. Hold one handle or loop a rope through the large eye and watch the wheel precess- and not fall over as you might expect it to. Gently balance the wheel on its handle like a top. You may also demonstrate some other common spinning toys and think about how they benefit from gyroscopic motion and stability.