Circular Motion

Newton's Second Law

applied to

Uniform Circular Motion

We have already looked at Uniform Circular Motion (UCM) and the idea of the center-seeking centripetal acceleration for any object moving in a circle. There, we found that, even tho' the speed remains constant, the velocity changes for any object moving in a circle. This means it has an acceleration. This is known as the centripetal acceleration,

ac = v2/r

and is directed toward the center of the circle.

From Newton's Second Law, F = m a, we now can look for the cause of this acceleration. The net force acting on an object moving in a circle must cause this acceleration. We can call this net force the centripetal force,

Fc = m ac

Fc = m v2/r

This centripetal force is the net force and is directed toward the center of the circle.

(The textbook gives several examples. They are all good. Be sure you understand all of them. We will look at only a few.)

What provides the centripetal force necessary for a car to make a curve on a flat road? What happens if that force is not present?

(You can test these ideas this winter -- but please be careful!)

Exit and entrance ramps to Interstate highways or freeways are usually banked. Why is that?
What forces act on the pilot of a plane -- or a guest on a loop-the-loop roller coaster -- as he or she makes various kinds of loops?

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(c) Doug Davis, 2001; all rights reserved