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A Proof of The relationships between the force, the mass, the speed, and the radius of an object moving in Uniform Circular Motion Consider an object moving in UCM. A r vA AB r B vB v vB vA Both triangles are isosceles. Since all three corresponding angles are congruent, the triangles are similar. Hence, corresponding sides are proportional. Fnet ma v a t vB v A a t v B v A a t v AB v r To make a a, let t 0 (In other words, move the points closer together) Results in AB Arc AB v Arc AB v r But since the object is moving at a constant speed d v t d vt Arc AB vt v vt v r 2 vt v r v v 2 t r v2 a r By Newton' s Second Law Fnet ma mv 2 F r No Error!