# Skater. Angular Momentum. Velocity.

## Homework Statement

10. A skater brings her arms in close to her body during a spin. What is the effect on her
angular momentum and angular velocity?

A) Angular momentum increases, velocity increases.
B) Angular momentum decreases, velocity decreases.
C) Angular momentum remains constant, velocity increases.
D) There is insufficient information to tell what will happen

L = Iω
ω = v / r

## The Attempt at a Solution

By bringing her arms in closer, she is decreasing the radius of her moment of inertia. As "r" gets smaller, v gets larger so ω becomes larger. When ω becomes larger, L is larger too because they're directly proportional. I choose "A." Do you all agree?

## Answers and Replies

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tms
No. What external forces are at work here? (I assume friction is being ignored.)

rcgldr
Homework Helper
By bringing her arms in closer, she is decreasing the radius of her moment of inertia.
and what effect does that have on her moment of inertia?

tms - Erm, gravity?

rcgldr - I = Mr^2 for a point mass so that decreases I.

ω * r = v

I just said "r" decreased. Perhaps letter "B" is a better choice.

rcgldr
Homework Helper
external forces
gravity?
Yes, but is that affecting the angular momentum? If no external force is affecting angular momentum, then what usually happens with angular momentum.

what happens when skater pull in her arms
I = Mr^2 for a point mass so that decreases I.
So what do you think happens with angular momentum?

rcgldr - When no external forces are acting, angular momentum is conserved. But if "I" decreases, "L" should too.

rcgldr
Homework Helper
rcgldr - When no external forces are acting, angular momentum is conserved. But if "I" decreases, "L" should too.
If angular momentum is conserved and "I" decreases, then what should happen with ω ?

Angular momentum must increase to compensate for that. I was thinking of "v" and not "ω." So if someone came along and pushed the skater, would that be an external force?

"C."

rcgldr
Homework Helper
If angular momentum is conserved and "I" decreases, then what should happen with ω ?
Angular momentum must increase to compensate for that.
Did you mean that angular velocity must increase (since angular momentum is conserved)?

C.is correct:angular momentum remains constant,velocity increase because radius decrease...

rcgldr - Yes. That's what I should have typed. Sorry about that.

tms
tms - Erm, gravity?
Which is exactly countered by the force of the ice on the skater, thus no net external force. Unless, perhaps, the skater is boring a hole through the ice, but I think we can ignore that possibility.