## Author(s)

Mark Pichaj

**Description of Equipment**

The gyroscope is spinning rotor mounted on low-friction bearings inside a gimbaled frame that allows the spin axis to be oriented in any direction.

* ** Here is a diagram of an typical gyroscope (from Wikipedia, of course).*

**Principles Illustrated**

Inertia and momentum, especially angular inertia and momentum, and the effects of friction.

**Photographs & Movies of Demonstrations**

(1) The operation of a gyroscope. *(All images and animations from Wikimedia Commons.)*

(a) Diagram of forces on a gyroscope:

(b) Animation of the effects of these forces:

(c) The operation of a free-spinning gyroscope:

(d) A operation of a gyroscope undergoing precession:

(2) Videos of gyroscope demonstrations. *(from youtube)*

(a) A tutorial about the gyroscope (from Science Online):

#### ScienceOnline Gyroscope Tutorial

(b) A demo of precession using a bicycle wheel (from MIT):

#### MIT Demo of Bicycle Wheel Precession

**Topics Addressed**

Big Ideas that explain the Gyroscope

** ***Momentum* (mass x velocity) is an easily-understood physical quantity. *Angular momentum*—not so much. Not everything in nature travels in straight lines; some things spin, too. The concept of angular momentum has to take into account not only mass and velocity, but the spin, as well. A **gyroscope **illustrates the concept of and shows the reality of angular momentum.

Angular momentum (**L**) can be calculated in several ways; here are two simple ones:

(1) **L** = I w

This means that angular momentum is the product of the rotational inertia of the spinning thing (*I*, in kilograms x meters x meters) and the angular velocity (w, in radians/second). Easy, right? Angular momentum just equals mass x velocity—or their rotational equivalents, at least. Hmm...maybe not so easy to understand.

(2) **L** = r x p

This way of calculating angular momentum makes more "sense." Think of angular momentum as a "twisting" momentum—a momentum that is being applied at a certain distance from a fulcrum (or axis) and in a perpendicular direction, much as **torque** is a force applied perpendicular to a distance from a fulcrum. Take the linear momentum (p, in kg x m/s) of the spinning thing ("rotor") at its edge (which takes some calculus—sorry—unless all the mass is concentrated perfectly at the very edge) and multiply it (by a "cross product"—again, sorry) by the distance from the axis (r, in meters). Since these two vectors are perpendicular to each other, the torque exerted on the gyroscope by the force by gravity x the distance from the axis causes the gyroscope to turn in that direction, or to "precess."

**Standards**

# Physics - Grades Nine Through Twelve

## Motion and Forces

- Newton's laws predict the motion of most objects. As a basis for
understanding this concept:
- Students know circular motion requires
the application of a constant force directed toward the center of the
circle
- * Students know how to resolve
two-dimensional vectors into their components and calculate the magnitude
and direction of a vector from its components.
- * Students know how to solve problems
in circular motion by using the formula for centripetal acceleration in
the following form: a=v2/r

## Conservation of Energy and Momentum

- The laws of conservation of energy and momentum provide a way to
predict and describe the movement of objects. As a basis for understanding
this concept:
- Students know how to calculate
momentum as the product mv.
- Students know momentum is a separately
conserved quantity different from energy.
- Students know an unbalanced force on
an object produces a change in its momentum.

**Study Guide Questions**

Club Knowledge Study Guide (an excellent resource for exploring gyroscopes): http://www.clubknowledge.com/study/gyro.html

**References and Links**

(1) The Gyroscope, from hyperphysics: http://hyperphysics.phy-astr.gsu.edu/HBASE/gyr.html

(2) The Gyroscope, from wikipedia: http://en.wikipedia.org/wiki/Gyroscope

(3) Torque: http://en.wikipedia.org/wiki/Torque

(4) Club Knowldge Gyroscope Study Guide: http://www.clubknowledge.com/study/gyro.html