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Rotation about a point

Question: There is a point mass rotating around a pivot. From what I understand, if the weight of the pivot is infinite, then in a frictionless environment the rotation of the point mass would never slow down. However, if the mass of the pivot was very light, then the pivot point would wobble as the centrifugal force of the point mass pulled it in different directions as it rotated. In this case, the point mass would slow down over time. So given the mass and angular velocity of the point mass and its radius from the pivot, and the mass of the pivot point, how quickly would the rotation of the point mass slow down in a frictionless environment?


Answer:

Isn't the set-up rather like a double star?
In one case one of the stars is very massive in comparison with the other and in the second case it is of comparable mass.

I agree that the "central" more massive star will move (but not really wobble) if its mass is not infinite but I do not agree that it will slow down. Both the objects will rotate about a common centre of mass and neither of them will slow down (in the absence of any external frictional forces).

This assumes that they are in a state of "equilibrium motion" as mentioned below.

The only case where I could imagine a "slowing down" is if the small (point) mass were suddenly to appear near to the larger mass, in that case there would be a period during which the motion would settle down into an equilibrium state but after that there would be no further slowing.

 
 
 
© Keith Gibbs 2013