This model is [generally applicable], but mathematically very complicated. In introductory mechanics it will only be used to describe the motion of a gyroscope.

Only used in problems involving a gyroscope.

• Angular Momentum and External Torque about a Single Axis
• Uniform Circular Motion

• torque (single-axis)
• angular momentum about a single axis

Technically, any number of rigid bodies. In practice, only used in analyzing gyroscopes (single rigid body with a fixed pivot point).

Only external torques need be considered. Internal torques do not change the system's angular momentum.

Gyroscopic Approximation

The gyroscopic approximation assumes that the angular momentum due to precession of the gyroscope is negligible compared to the angular momentum of the spinning gyroscope. If Ω is the angular velocity of precession and ω is the angular velocity of the gyroscope's spin, then the gyroscopic approximation holds when

and

I is the moment of inertia of the gyroscope about the spin axis

See Spinning Top and Delta-v diagram for more details.

Angular Frequency of Gyroscopic Precession

Under the gyroscopic approximation, the angular velocity of the precession is given by Ω

This result is independent of the tipping angle of the gyroscope.

Differential Form

• A delta-L diagram analogous to the Delta-v diagram of Uniform Circular Motion.

• Spinning Top