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Answer to Question #6228 in Mechanics | Relativity for Stephen

Question #6228
A ball rolls off a frictionless sphere with neglible inital velocity, at what point does the ball fall off?
1
2012-02-02T11:03:52-0500
The forces on the ball include the centripetal force due to gravity, the centrifugal force due to motion along the curve and the resulting normal force
The gain in kinetic energy as the bug slides is provided by the loss in
potential energy. Since
<img src="data:image/png;base64,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" alt="">
we have
At the moment the ball leaves the ball, the normal force Fn becomes zero. We can now substitute the value of the centrifugal force

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