A figure skater spins with her arms stretched wide. Then she pulls her arms in to her chest, and with no extra kick and no outside help she spins visibly faster. Nothing touched her.
Where did the extra spin rate come from?
From her own shape. The skater carries angular momentum, and with no outside twist acting on her, that carried amount cannot change. What can change is how her mass sits around the spin axis.
Run it on the skater. Arms wide, her mass sits far from the axis: she turns slowly.
She pulls her arms in. Her mass moves close to the axis, and her angular momentum stays constant, because no outside twist acts. So her spin rate rises.
She stretches her arms out again, her mass moves away from the axis, and the same constant angular momentum now turns her slowly.
Nothing was added and nothing was lost. The carried amount of rotation stayed the same. Her shape traded between a slow wide spin and a fast narrow one.
The condition matters, and it is about twists, not rates. The rule holds while no outside twist acts on the spinning object: a hand grabbing the skater, or a rough surface dragging on a spinning wheel, is an outside twist, and then the angular momentum does change.
Notice what the condition is not. A constant spin rate is not the condition: the skater's rate rose while her angular momentum stayed constant. A steady spin rate can be evidence that no outside twist acts, but the condition itself is the absence of the outside twist.
A diver somersaults in the air, stretched out, then pulls into a tight tuck. What happens to her somersault rate?
Odile sits on a free-spinning swivel stool holding two heavy books at arm's length, turning slowly. She pulls the books in to her chest. What happens to her spin rate, and why?
No outside twist acts on Odile on the free-spinning stool, so her angular momentum stays constant.
Pulling the books in moves mass closer to the spin axis.
For the same angular momentum, mass closer to the axis means a faster turn.
Her spin rate rises: the carried angular momentum is unchanged, and her mass now sits closer to the axis.
A dancer spinning on one foot pulls her arms in and turns faster. Why?
A diver leaves the board in a tight tuck, somersaulting quickly. Before entering the water she stretches out straight. What happens to her somersault rate, and why?
In the air no outside twist acts on the diver, so her angular momentum stays constant.
Stretching out moves her mass farther from the rotation axis.
For the same angular momentum, mass farther from the axis means a slower turn.
Her somersault rate falls: the carried angular momentum is unchanged, and her mass now sits farther from the axis.
Pavel says: 'A spinning figure skater who stretches her arms out while spinning slows her spin.' Is he correct?
A gymnast somersaulting in a tight tuck opens out straight before landing. What happens to her rotation rate while she is still in the air?
Two kids stand at the edge of a playground spinner that is turning freely. They walk from the edge toward its center. What happens to the spinner's turning rate?
Under which condition does a spinning object's angular momentum stay constant?