Skater. Angular Momentum. Velocity.

1. Apr 3, 2012

PeachBanana

1. The problem statement, all variables and given/known data

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

2. Relevant equations

L = Iω
ω = v / r

3. 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?

2. Apr 3, 2012

tms

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

3. Apr 3, 2012

rcgldr

and what effect does that have on her moment of inertia?

4. Apr 3, 2012

PeachBanana

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.

5. Apr 3, 2012

rcgldr

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

So what do you think happens with angular momentum?

6. Apr 4, 2012

PeachBanana

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

7. Apr 4, 2012

rcgldr

If angular momentum is conserved and "I" decreases, then what should happen with ω ?

8. Apr 4, 2012

PeachBanana

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."

9. Apr 4, 2012

rcgldr

Did you mean that angular velocity must increase (since angular momentum is conserved)?

10. Apr 4, 2012

nicu

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

11. Apr 4, 2012

PeachBanana

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

12. Apr 4, 2012

tms

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.