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If we consider a ball attached to a string that moves in a circle at a constant speed, then in a ball-Earth system: the kinetic energy doesn't change, the string does zero work, and yet the gravitational potential energy is not the same throughout (for example, it's double at the top what it is at the bottom).

How can this be, if the system is isolated? I get that the ball doesn't have to move at a constant speed; I'm just confused about when it does.

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    $\begingroup$ Yes, I would also be confused if a ball on a string was moving in a vertical circle and traversed the circle at constant speed. But that's not how the ball will move. (If this doesn't clear things up, could you please clarify your question.) $\endgroup$
    – tom10
    Feb 24, 2021 at 23:02
  • $\begingroup$ @tom10 Oh, I was under the impression that it would be possible for the ball to move uniformly. What would be another setup where it would not be possible for an object to move at constant speed? $\endgroup$
    – user13315799
    Feb 25, 2021 at 3:33
  • $\begingroup$ Gravity creates an acceleration and acceleration is the definition of non-constant speed. So other situations where it's not possible for an object to move at constant speed are any other situations where the object is also experiencing an acceleration. Some other ways an object might be undergoing an acceleration are if it's being mechanically accelerated (like in an accelerating car or rocket or attached to a spring), or if it's charged and in an electric field, etc. $\endgroup$
    – tom10
    Feb 25, 2021 at 3:41

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Very easy, the situation is not physical. The ball must be slower at the top or you need to accelerate/decelerate it as it goes up/down. Of course, the difference in speed is very small, so you probably cant see it with the naked eye.

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  • $\begingroup$ If it just barely makes it, you can see the slow down. $\endgroup$
    – DJohnM
    Feb 25, 2021 at 1:15

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