Angular Momentum conserved with friction?

[theRIAA]

This was a conceptual question on my physics exam:

True or false: You drop a non-rotating disk onto a rotating disk. When they hit they slide against each other with friction for a few seconds before they both start rotating at the same rate together. Because of losses due to that friction, angular momentum will NOT be conserved. (No other information was given)

I put True, the "correct" answer was False.

Am I wrong? Won't energy be lost as heat and sound through friction?

 

[tiny-tim]

Welcome to PF!

Hi theRIAA! Welcome to PF!

Am I wrong? Won't energy be lost as heat and sound through friction?

D'oh!

Yes, you're absolutely right … but you haven't answered the question!

The question asks about angular momentum, and you've answered (correctly) about energy.

Energy behaves completely separately from both ordinary and angular momentum.

Angular momentum (about a point) is always conserved (provided there is no external torque about the point, and in this case they asked you only to consider the effects of the friction between the discs, which is internal ).

 

[theRIAA]

Hi theRIAA! Welcome to PF!
Angular momentum (about a point) is always conserved (provided there is no external torque about the point, and in this case they asked you only to consider the effects of the friction between the discs, which is internal ).

so.. even if the disks make a thunderous grinding sound and shot off sparks for an hour before spinning together... they will still end up with the same angular velocity as ones that made hardly any sound at all? I understand force and momentum act differently.. but isn't some momentum lost?

 

[tiny-tim]

Momentum is for ever.

Without an external force in that direction, it can't be lost.

Angular momentum is for ever..

Without an external torque about that point, it can't be lost.

Of course, sparks shooting off will carry away angular momentum. ​

 

[theRIAA]

I'm assuming friction is non-conservative. Some of this friction force from is transferred to the disks, while the rest is converted into heat and sound. This non-conservative friction is the external force in the direction opposite to momentum.

I refuse to believe friction plays no role unless someone logically explains how an unlimited amount of sound and heat can be produced without effecting the final angular velocity in this problem.

 

[tiny-tim]

This non-conservative friction is the external force in the direction opposite to momentum.

Yes, it is non-conservative.

But it's not external.

 

[theRIAA]

the sound waves created heat up the environment, the environment is external...

 

[tiny-tim]

the sound waves created heat up the environment, the environment is external...

Sound is omni-directional, so how can it carry away (net) angular momentum?

 

[theRIAA]

Sound waves are converted from angular momentum, into energy by friction. Friction is caused by vibrations of the disks.The disks vibrate to create sound by pushing against air molecules. air has weight, vibrations use momentum.

 

[tiny-tim]

(just got up :zzz: …)

… air has weight, vibrations use momentum.

Still omni-directional.