6.2 Uniform Circular Motion

Qualitatively, a force in the centripetal direction is what’s needed for uniform circular motion.

Explanation at xmdemo.wordpress.com/124

Quantitatively, the magnitude of the required centripetal force is related to the speed and radius of circular motion by the formula F=mv2/r.

centripetalForce0

On the other hand, 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 4F, 2F and F, resulting in circular motion of radii R, 2R and 4R.

centripetalForce1

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 √2v, resulting in circular motion of radii R, 2R and 4R.

centripetalForce

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