Conservation of Angular Momentum

[benny1993]

Suppose I have a system of two disks (identical in mass and size) one is fixed to a shaft at it's center point and rotating due to an external torque that's removed as soon as the rotational motion begins. The second disk is dropped from rest over the rotating disk and sticks together to the rotating disk. What would be the force that generates the torque that accelerates the disks during the collision?
If there are no external forces acting on the system (since the accelerating external force is removed as soon as motion begins), the net torque has to equal zero. I don't get what other force actually causes the torque the accelerates the already rotating disk (which would be decreasing) and the torque that accelerates the dropped disk?

 

[anorlunda]

Friction is the force as the two disks touch each other.

But I think the question you're really looking for is conservation of momentum for the two-disk system.

 

[benny1993]

So is the torque that rotates the stationary disk is caused by the force of friction? The next questions asks to explain why this torque (that rotates both disks) can't account for experimental discrepancies between the final and initial angular momentum, given that we neglected friction in the experiment.

 

[anorlunda]

Summary: Lab Question on Angular Momentum Conservation.

What would be the force that generates the torque that accelerates the disks during the collision?

If I picture it right, one disk accelerates and the other decelerates. After a brief time, they rotate at the same speed. If that's not it, can you describe it better?

 

[benny1993]

That's exactly how the experiment goes. One disk is rotating while the other is dropped from rest. Immediately after, they both begin to rotate at the same speed.

 

[jartsa]

The rough surface of the static disk receives a large number of small hammer blows from the rough surface of the spinning disk. I mean the small hammers are spinning around.

If the disk is dropped from high position, then the torque is very large and lasts a very short time. I mean the torque caused by the hammer blows.

If the disk are smooth and sticky instead of hard and rough, then the story must be changed somehow.


Oh, it was already agreed that friction is the cause of the force. Maybe the above is redundant then. So, is the final thing (two disks stuck together) not spinning at half of the upper disk's original speed? And with the same angularar momentum? And at half of the energy?

 

[zanick]

Summary: Lab Question on Angular Momentum Conservation.

Suppose I have a system of two disks (identical in mass and size) one is fixed to a shaft at it's center point and rotating due to an external torque that's removed as soon as the rotational motion begins. The second disk is dropped from rest over the rotating disk and sticks together to the rotating disk. What would be the force that generates the torque that accelerates the disks during the collision?
If there are no external forces acting on the system (since the accelerating external force is removed as soon as motion begins), the net torque has to equal zero. I don't get what other force actually causes the torque the accelerates the already rotating disk (which would be decreasing) and the torque that accelerates the dropped disk?

you have the moving disc and the one dropped on it.. the friction will be a force that decelerates the bottom disc and accelerates the upper disc, so there is an exchange of momentum through the friction. besides the loses in friction , noise and heat, the net momentum will remain constant (minus that small value of the momentum of the shaft the bottom disc has) which will spin up the upper disk and slow down angularly , the bottom disc.

 

[A.T.]

Next questions asks to explain why this torque (that rotates both disks) can't account for experimental discrepancies between the final and initial angular momentum, given that we neglected friction in the experiment.

The torque between the disks is internal and does not change the angular momentum of the two disk system. The external torques come from friction at the bearings and beteween disks and air.

 

[sophiecentaur]

Oh, it was already agreed that friction is the cause of the force. Maybe the above is redundant then. So, is the final thing (two disks stuck together) not spinning at half of the upper disk's original speed? And with the same angularar momentum? And at half of the energy?

Woops! Rotational energy is given by Iω²/2 so, although the Momentum is conserved, the total final Energy will be Half the original. (Two times one quarter) The energy went away due to the friction, whatever the friction force happens to be. It will just take longer or less time to reach equal speeds, depending.
This paradoxical looking result is a common sort of result that you get with many other idealised systems. The best known example is what happens when you connect two Capacitors (one charged and one discharged) together. Again you lose half the energy,

 

[zanick]

excellent!