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# Illustration 5.3: The Ferris Wheel

Please wait for the animation to completely load.

So how does our analysis of Newton's laws change when an object is moving in uniform circular motion? There are really only two things to remember.

First, the net force is always toward the center of the circle for uniform circular motion. This net force is responsible for the acceleration toward the center of the circle, the centripetal acceleration we saw in Illustration 5.2.

Second, because the centripetal acceleration is a positive number, v^{2}/r, it can never be negative. So unlike linear motion in which you have a choice of where to place the coordinate axes (to make life easier or more difficult), the choice here is critical. Your choice of coordinates must have one axis with its positive direction pointing toward the center of the circle.

In the animation, a Ferris wheel rotates at constant speed as shown **(position is shown in meters and time is shown in minutes)**. Each square represents a chair on the Ferris wheel. Restart.

Consider a rider at point (a). What does the free-body diagram for a chair on the Ferris wheel look like at this point? To answer this question we must determine the applied forces that act on a rider when the rider is at point (a). At point (a) there are the normal force and the weight acting in opposite directions. Are the forces the same size or different? They must be different and the normal force must be bigger. Why? We know that the net force must point toward the center of the circle and that the net force is ma = m v^{2}/r for uniform circular motion.

What is the acceleration of the rider when the rider is at point (a)? As stated above we know the acceleration must be v^{2}/r, where v = 2πr/T, where T is the period of one revolution.

What about the answers to these questions when the rider is at points (b), (c), and (d)? Well, the forces may be different or point in different directions, but the results are the same. The net force must be toward the center of the circle and be m v^{2}/r.

Illustration authored by Mario Belloni.

Script authored by Aaron Titus.

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