Q] Using the energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Is zero speed possible at the uppermost point? Under what conditions? Also prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the object.
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Yes, at the uppermost point, the zero speed is possible in the trajectory. The vertical velocity becomes zero under the conditions, where velocity direction completely stays horizontal and the acceleration remains downwards because of the gravity. Hence, the angle we get is called π/2.
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