Conservation of Angular Momentum

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Discussion Overview

The discussion revolves around the conservation of angular momentum in a system involving two disks, one fixed and rotating, and the other dropped onto it. Participants explore the forces and torques involved during the collision and the implications for angular momentum and energy conservation, particularly in the context of experimental discrepancies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the source of torque that accelerates the disks during the collision, noting that external forces are removed and the net torque should equal zero.
  • Another participant suggests that friction is the force responsible for the torque as the disks come into contact.
  • A participant seeks clarification on whether the torque that rotates the stationary disk is indeed caused by friction and raises concerns about discrepancies between initial and final angular momentum when neglecting friction.
  • One participant summarizes the process, indicating that one disk accelerates while the other decelerates until they rotate at the same speed.
  • Another participant describes the interaction as involving "hammer blows" from the rough surface of the spinning disk, emphasizing the role of torque and friction in the process.
  • Discussion includes the idea that while momentum is conserved, energy may not be, particularly due to frictional losses, leading to a potential paradox in energy distribution.
  • Concerns are raised about whether the final state of the disks results in them spinning at half the speed of the upper disk and the implications for angular momentum and energy conservation.

Areas of Agreement / Disagreement

Participants generally agree that friction plays a crucial role in the interaction between the disks, but there are varying interpretations regarding the implications for angular momentum and energy conservation. The discussion remains unresolved regarding the exact nature of the torque and its effects on the system.

Contextual Notes

Participants note that the torque between the disks is internal and does not affect the overall angular momentum of the system. However, external torques from friction at bearings and between disks and air are acknowledged as factors that could influence the results.

Who May Find This Useful

This discussion may be of interest to those studying angular momentum, frictional forces in rotational systems, and the implications of energy conservation in experimental physics.

benny1993
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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?
 
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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.
 
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.
 
benny1993 said:
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?
 
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.
 
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?
 
Last edited:
benny1993 said:
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.
 
benny1993 said:
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.
 
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jartsa said:
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,
 
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excellent!
 

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