# Bicycle Wheel as a Gyroscope

**Bicycle Wheel as a Gyroscope**is a common method of using a familiar object to demonstrate a counterintuitive physics concept. When spun and held by the rope, the wheel will seem to defy gravity due to gyroscopic precession.

This demo tends to be at a conceptually higher level than K-12 will address in their physics/physics-equivalent courses, but is neat nonetheless. This is a good introduction to angular momentum and can be shown before using the angular momentum stool.

To understand torque-induced precession, we must start by looking at the relationship between angular momentum and torque. Angular momentum is a vector quantity dependent on an object’s moment of inertia and angular velocity. Torque is also a vector quantity that represents the amount of force necessary to rotate an object along a given axis. These two quantities are directionally perpendicular to one another. The torque causes a change in *direction* of the angular momentum, but the *magnitude* remains unchanged. Thus, the bicycle wheel is able to spin gyroscopically, or precess, along its horizontal rotational axis in opposition to its vertical rotational axis.^{[1]}

$$\tau=mgl=I\alpha={{\Delta L}\over {\Delta t}} $$

Where $\tau$ is the torque due to the weight of the wheel, $l$ is the lever arm of the bicycle wheel, and $\alpha$ is the new angular momentum caused by the torque.

Additional information on precession can be found on the Precession Wikipedia page.^{[2]}

As previously mentioned, this demo is one of the more difficult ones to explain to a K-12 audience. It’d be best to avoid going in-depth about the math involved in order to keep the students’ attention. I like to relate the bicycle wheel to a spinning top, except we’re viewing it “sideways”. Using the spinning top mini demo (the Beyblade-esque one) wouldn’t hurt, just to give the students a visual example of something they’ve more than likely already seen before. While holding the bicycle wheel, I occasionally ask them, “what is this?” It’s a basic question, but I like to give them things that are easily answerable, especially if we’ll be dealing with a more difficult topic.

If the students are older, I briefly describe what angular momentum and torque are. I’ve found that describing torque simply as a “rotational force” or “a force to make something rotate” is sufficient. It may even be easier to focus/emphasize how these two quantities are vectors, and describe precession as the result of two vectors/directions being perpendicular to each other.

For younger students, I treat it more as a neat party trick. I rarely bring up this demo unless it is a caveat for the angular momentum stool. In this case, I briefly describe angular momentum, do the demonstration, and ask them to describe the motion of the wheel itself, as well as the motion of the system as a whole.

## Tips

**Some Leading Questions**- "Have you ever spun a top before? If not, have you ever seen a spinning top? How/Why do you think it’s staying upright?"

**Good Demos Before/After**- Spinning Top
- Angular Momentum Stool
- (More Periphery:)Spinning Cup
- This addresses inertia and would only be a good tie-in if you are planning on touching on the moment of inertia of the bicycle wheel with respect to angular momentum.