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Quantitatively, the magnitude of the required centripetal force is related to the speed and radius of circular motion by the formula *F*=*mv*^{2}/*r*.

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For the same *v*, a stronger centripetal force *F* would result in a tighter circular motion (smaller *r*). In the animation below, the objects are experiencing centripetal forces of 4*F*, 2*F* and *F*, resulting in circular motion of radii *R*, 2*R* and 4*R*.

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For the same centripetal force *F*, a lower speed *v* would result in a tighter circular motion (smaller *r*). In the animation below, the objects have speeds of 1/√2 *v*, *v* and √2*v*, resulting in circular motion of radii *R*, 2*R* and 4*R*.