friction acting on a spinning ice skater

[angelina]

when talking about conservation of angular momentum of a spinning ice skater, the contact surfaces are assumed to be frictionless. why?

[Physics_wiz]

Well, if there is friction to slow the skater down then his/her velocity would go down and decrease the angular momentum so it wouldn't be conserved.

[Tide]

when talking about conservation of angular momentum of a spinning ice skater, the contact surfaces are assumed to be frictionless. why?

A frictionless surface is assumed simply because it's a lot easier to analyze. However, the inclusion of friction does not alter the fact that total angular momentum is conserved.

[Physics_wiz]

Opps. Sorry, Tide probably knows what he's talking about more than me. Real sorry about that, but I just looked at the equation and saw mvr. r and m are constants so I thought, if v goes down, momentum goes down....eh I'm wrong anyways; listen to Tide.

[angelina]

A frictionless surface is assumed simply because it's a lot easier to analyze. However, the inclusion of friction does not alter the fact that total angular momentum is conserved.
*total* angular momentum means the system of the skater alone or the system of the skater + ice floor?

also, say the spinning direction is on the x-z plane, then the friction acting on will be providing a torque along the x-direction. my question is, how does this frictional torque affecting the angular momentum of the skater??

[Doc Al]

If there is friction between the ice and skate, then the ice will apply a torque to the skater, reducing her angular momentum. Of course, if you include both the skater and the ice floor in your system, then angular momentum is conserved.

[angelina]

If there is friction between the ice and skate, then the ice will apply a torque to the skater, reducing her angular momentum. Of course, if you include both the skater and the ice floor in your system, then angular momentum is conserved.
then my question will become - is it true that as longer as there's external torque, no matter this torque is acting about the same axis as the rotation or about a different axis, angular momentum is not conserved??

[Doc Al]

Right. If there is an net external torque, then total angular momentum is not conserved. But it is often the case that you can conserve angular momentum about a particular axis.

In the case of the spinning skater, her axis of rotation is vertical, and, assuming no friction, there is no torque about that vertical axis. So her angular momentum about that axis is conserved.

[angelina]

Right. If there is an net external torque, then total angular momentum is not conserved. But it is often the case that you can conserve angular momentum about a particular axis.

In the case of the spinning skater, her axis of rotation is vertical, and, assuming no friction, there is no torque about that vertical axis. So her angular momentum about that axis is conserved.
for the case of the spinning skater, if friction exists, which axis will its torque act about? the same vertical (y-axis) or the z-axis or both??

[Doc Al]

If the skater spins about the vertical axis, then the friction (which opposes the motion of her skates) will exert a torque about that same vertical axis.

[Andre]

And what happens to the "lost" momentum due to the friction? It is added to the rotation of the Earth.

Actually the law of conservation of momentum is applying only to the complete universe, not individual systems. Systems interact. The moon and earth exchange momentum due to torque forces exerted by gravity.