If a bike rider constantly keeps rotating on a vertical circular path, what is the required minimum velocity on the highest point of the circle to keep him on the circular path without falling?
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$\begingroup$ Possible duplicate of: physics.stackexchange.com/q/245568 $\endgroup$– GertCommented Feb 17, 2019 at 15:37
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$\begingroup$ The friction force must be greater or equal to the centrifugal force $\mu\,{m\,g}\geq \dfrac {mv^{2}}{r}$ $\endgroup$– EliCommented Feb 17, 2019 at 15:42
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1 Answer
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Assuming the rider is travelling inside the edge of the circle then at minimum velocity the centripetal force maintaining the circular path at the top is the weight of the rider. Therefore $$mg = \frac{mv^2}{r}$$ which gives $$v = \sqrt (gr)$$ where $g = 9.81 ms^{-2}$ and $r =$ the radius of the circle.
