Rotational kinetic energy explaination

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Discussion Overview

The discussion revolves around the concept of rotational kinetic energy, particularly in the context of two different experiments involving conservation of angular momentum. Participants explore the implications of changing the moment of inertia on angular speed and kinetic energy, questioning the source of energy in a scenario where no additional energy input seems to occur.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a classroom demonstration involving a rotating stool and weights, explaining how pulling arms in increases angular speed and kinetic energy due to conservation of angular momentum.
  • The same participant presents a different scenario with a volleyball tethered to a pole, where striking the ball gives it energy, and as the string wraps around the pole, the moment of inertia decreases, leading to a doubling of angular speed and kinetic energy without additional energy input.
  • Another participant responds by stating that work is done by the tension in the string, which is necessary for the changes in motion, but does not clarify the source of the energy given to the volleyball.
  • A further response questions the explanation, emphasizing that a source of energy must exist to cause the tension in the string, and expresses discomfort with the idea of the string exerting energy without an external influence.

Areas of Agreement / Disagreement

Participants express differing views on the source of energy in the volleyball scenario. While some acknowledge the role of tension in the string, others challenge the notion that this tension can exist without an external energy source, indicating a lack of consensus on the explanation.

Contextual Notes

The discussion highlights the complexity of energy transfer in rotational dynamics and the assumptions regarding energy sources in mechanical systems. Participants do not reach a resolution on the source of energy in the volleyball example.

  • #91
aaaa202 said:
hmm it's just that when you see the ball for the point of contact between string and pole it makes a uniform circular motion. So can't you say that the angular momentum is conserved in this frame for the ball? And why does that not qualify to the ball's angular momentum being conserved like if the rotation was around the center of mass? :)

The point of contact is changing all the time: it's turning in a circle around the pole, so (as Philip pointed out) it's constantly accelerating. If we fix one point on the surface of the pole and measure the angular momentum around this point, we'll see that the momentum of the ball must be changing, since there is only one instant when the ball exerts no torque in this frame: the instant when the centre of rotation is at the point we have fixed. For the rest of the time, the centre of rotation is not at the point we have fixed, so there is torque around this point.
 
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  • #92
yes okay, I should have realized that. But doesn't there exist conservation laws in non inertial reference frames?
 
  • #93
I expect so. Indeed I expect we could easily find such a frame in which angular momentum is conserved for the ball. But that would not be anything to be especially pleased about. The ball's angular momentum would be conserved simply because we've chosen a special frame in which it is conserved. In this frame, things whose angular momentum we'd normally expect to be conserved won't have it conserved... The laws of Physics are usually easier in inertial frames.
 

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