Angular momentum and centripetal force

  • #1
Suppose you have a ball on a string, and you make the ball to move around in a circle. The force on the ball is caused by the tension of the string, and is called the centripetal force F = mv^2/r. If you were to let go at any moment, the ball would stop rotating and move with linear velocity.

Now suppose you had a disk on a pole, and you make the disk rotate at constant angular velocity. According to the conservation of angular momentum, the disk would keep on rotating at the same speed (assuming no external torque). My question is, if you focus on only one point on the disk, is it correct to say that the point is in circular/centripetal motion, and therefore is no different than a ball on a string?

If that is so, then there must be a centripetal force making that point move in a circle. For the case of the ball on the string, the human (and by extension the string) is the ultimate "source" of the centripetal force. What is the "source" for the disk, and why doesn't it exist for the ball on the string when the human lets their grip off the string?

I've been a bit rusty with mechanics, so it's possible I'm just misunderstanding.
 

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  • #2
andrewkirk
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The centripetal force on the point on the disk is provided by the electrostatic forces that keep the disk structurally solid. You can consider the strip of disk material between the point and the centre of the disk as performing broadly the same role as the string does in the case of a ball on a string.

The letting go of the string is analogous to the disintegration of a flywheel when it spins too fast. The centrifugal (pseudo-)forces become too great for the electrostatic structural binding forces of the flywheel material to resist and it flies apart.
 
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  • #3
Thanks, that made it a little clearer.

One thing I still don't get is why the string attached to the ball doesn't count as an an extended object held together by electrostatic forces (and therefore could generate centripetal forces without aid of a human). Is it because of the "structurally solid" requirement you made? Does that mean the string has to be hard to bend? (well you'd probably not call it a "string" then, ha). Is there a quantitavie way to measure that? Also does the string have to have a reasonably sized mass compared to the ball?

Secondly, does that mean when we say "a point mass has moment of inertia I = mr^2",we don't literally mean protons and electrons, since the electrostatic argument wouldn't hold? (what I know from quantum seems to suggest that's the case).
 
  • #4
andrewkirk
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One thing I still don't get is why the string attached to the ball doesn't count as an an extended object held together by electrostatic forces (and therefore could generate centripetal forces without aid of a human).
I don't understand the question. There is no need for a human in the string and ball experiment. The string could be simply tied to a pivot and the ball launched into a circular path by a machine. In the case of both the string and a solid disk, it is the tensile strength (as opposed to compressive strength) of the material that enables transmission of centripetal force.
 
  • #5
I didn't mean that there was a need for a human, I only said human because that was the example I gave.

But anyways, you answered the question so thank you.
 
  • #6
CWatters
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In case it helps... if you replace the string with a rigid wire the two situations are essentially identical.
 

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