Where to Go From Here
- An introduction to angular momentum
- Example: Halting a spinning record
- Example: The skater
- Angular momentum formulas
- Quiz yourself on angular momentum
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Where to Go From Here
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Angular momentum is related to how something moves around a point. All moving objects have some sort of angular momentum but it is used most often to describe rotating objects. We will only be discussing angular momentum as it related to rotation. Forces in certain directions can change the angular momentum of an object. Just like with linear momentum, the greater the mass of an object and the faster it is moving, the more difficult it is to slow down and stop the movement and rotation.
Example: Halting a Spinning Record
It also makes a difference where you apply the force to slow the
rotation down. For instance, if you want to stop a record that
is spinning on a turntable by pressing your finger down and using
the friction between you finger and the record to slow the
spinning, how quickly the record comes to a stop depends on where
you put your finger down. If you press down right at the center
of the record (called the axis of rotation), the spinning will
not be affected. You must put your finger somewhere else on the
record to affect the spinning. If you put your finger down close
to the center, the spinning will stop but only if you push down
hard for a while. When you move you finger closer to the edge of
the record, the spinning will stop more quickly.
Angular momentum can be seen in an ice skater's spin. He starts
the spin with his arms extended and then pulls them in. His speed
becomes faster as he pulls in his arms. The angular momentum of the
skater is conserved. The distance his hands are from the center of
his body (the location of the axis of rotation) controls how fast he
spins. When angular momentum stays constant, velocity is inversely
proportional to the distance of the object from the axis of rotation;
when the distance goes down, the velocity goes up and vice versa. In
the case with the skater, his hands are the objects and as he pulls
them in, his spinning gets faster. He slows down by letting his arms
back out.
Angular momentum is conserved when no force is acting to change the rotation. In the real world, few things have perfectly conserved angular momentum. The angular momentum of a spinning top is nearly conserved. It will spin for a very long time but will eventually slow down and tip over. There is friction where the top's support is rubbing against the floor and the angular momentum is changed by the friction ever so slightly. The effect is so slight that we can say the angular momentum of the top is conserved, at least for a time period right after you start it spinning. In other spinning systems, like the skater or a yo-yo, friction affects the angular momentum slightly. For a short period of time right after the spinning starts, angular momentum in these systems is considered to be conserved.
Angular Momentum FormulasAngular momentum for a spinning or rotating object is equal to
