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Work is equal to Force * displacement * cos(angle between force and displacement). When there is uniform circular motion, the displacement is in the same direction as the velocity: along the tangent of the circle. The centripetal force always points towards the center of the circle. These two directions (vectors) are perpendicular to each other (90 degrees). Cos(90) = 0, so the work is 0.

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Is acceleration uniform in uniformly circular motion?

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