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What's the slowest speed?

A frictionless rollercoaster does a vertical loop with a radius of 6.0 m. What's the slowest speed that the rollercoaster must have at the top of the loop and avoid falling?
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1 Answer

It won't fall if the velocity is high enough so that centripetal acceleration, a, is at least g, acceleration of gravity.
Thus, g=a=v2/R; So v=√(gR)=√(9.8*6)=√58.8≈7.7 m/s