Spinning Your Wheels : A Lesson by Mathalicious

Have you ever noticed that the wheels in car commercials sometimes look like they’re spinning backwards? Is this some sort of fluke in the tire design, or is something else going on?

In this lesson, students apply the formula for the circumference of a circle to convert between a car’s speed in miles per hour and the number of rotations its tires make every second. By comparing this rotational speed to the frame rate of a video camera, they’ll come up with rules to determine what makes a spinning wheel sometimes look like it’s moving in the opposite direction of the car sitting on top of it.

Students will

Convert between different units of speed (miles per hour, inches per second, and inches per frame of video)
Calculate the circumference of a tire, given its diameter
Convert between speed of a car and rotational speed of its wheels
Determine whether a wheel will look like its spinning forwards or backwards, based on its rotational speed
Predict how the tire of an accelerating car will appear to spin on film

Before you begin

Students will need to perform a lot of unit conversion in this lesson, so some previous experience will be helpful (e.g. the ability to convert a speed in miles per hour to feet per second). Students should also know the formula for the circumference, C, of a circle of radius r (C = 2πr).