Circular Motion Application

As I said in my previous post, I am going to expand on the physics behind Ferris wheels, and vertical circular motion in general. For Ferris wheels, it is important to first draw a free body diagram of the forces acting on a person sitting in the chair. It is also important to realize that the centripetal acceleration will still be in the direction of the center of the circle, therefore the magnitude of forces are different depending on whether you are sitting at the top or the bottom of the ferries wheel.

http://jesseenterprises.net/amsci/1983/10/1983-10-fs.html

If the person is sitting at the top of the rotation, there are 2 forces acting on the person, gravitational force (Fg) and normal force (Fn). At the top of the circle, the centripetal force (Fc) is downward, into the center of the circle. In the previous post, I wrote that Fc is the vector sum of all the forces on an object moving in circular motion. This means that Fn and Fg are not the same magnitude because Fg must be larger, as there is centripetal acceleration. 

http://www.chegg.com/homework-help/questions-and-answers/figure-shows-ferris-wheel-rotates-times-minute-carries-car-circle-diameter-180-m-force-mag-q2985616

In contrast, when the person is sitting at the bottom of the rotation, the Fc is upwards, which means that the magnitude of Fn is larger than Fg. This explains why on a ferris wheel, people feel light at the top, and heavy at the bottom. To solve these types of problems, we first need to recognize which force is larger, and then can use the equation for Ac to solve. For example, if the person is sitting at the top of the ferris wheel, Fc= Fn-Fg, which means that Fn=Fg+mAc, which proves that the top of the ferris wheel, Fn<Fg.