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Circular Motion: Modelling a ferris wheel

This is a nice simple example of how the Tracker software can be used to demonstrate the circular motion of a Ferris wheel.  This is sometimes asked in IB maths exams – so it’s nice to get a visual representation of what is happening.

First I took a video from youtube of a Ferris wheel, loaded it into Tracker, and then used the program to track the position of a single carriage as it moved around the circle.  I then used Tracker’s graphing capabilities to plot the height of the carriage (y) against time (t).  This produces the following graph:

As we can see this is a pretty good fit for a sine curve. So let’s use the regression tool to find what curve fits this:

The pink curve with the equation:

y = -116.1sin(0.6718t+2.19)

fits reasonably well.  If we had the original dimensions of the wheel we could scale this so the y scale represented the metres off the ground of the carriage.

There we go!  Short and simple, but a nice starting point for an investigation on circular motion.

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