Rotation & Angular Dynamics · Physics

A torque can make a spinning axis turn sideways.

Gyroscopes and spinning tops respond to torque in a counterintuitive way: instead of tipping over directly, they often precess. This topic builds qualitative intuition using angular momentum vectors.

This topic

Gyroscopic Motion (Intro)

Understand precession as a direction change of L caused by torque, then interpret the common top/gyroscope scenarios.

Idea

Torque turns the angular momentum vector

The key idea is vector change: a torque produces a change in angular momentum, often changing its direction more than its magnitude.

Core link: Στ = dL/dt (vector idea)
Small dL added to L gives a new direction
Why the response can be “sideways”
Magnitude vs direction changes

Scenario

Why a spinning top doesn’t simply fall

Gravity provides a torque about the contact point. For a rapidly spinning top, that torque mainly changes the direction of L, producing precession rather than a simple tip-over.

Gravity torque about the pivot
L approximately along the spin axis
Torque changes L sideways → axis sweeps around
What happens as spin slows (qualitative)

Intro model

Precession idea (qualitative)

Precession is the slow rotation of the spin axis around a vertical line. You can predict the direction of precession with right-hand rule reasoning on τ and L.

Precession axis and direction (right-hand rule)
What “steady precession” means (conceptually)
Why larger L tends to mean slower precession
Limits: when the simple picture breaks down

Pitfalls

Common misconceptions

Gyro problems go wrong when the axis, torque direction, or the meaning of “stability” is misunderstood. Clear diagrams prevent most confusion.

“Torque equals tipping” misconception
Forgetting L is a vector
Mixing up spin and precession directions
Ignoring that friction and losses change behavior

Practice

Practice & Exercises

Practice using right-hand rule reasoning to predict precession direction, and interpreting how spin strength affects stability.

Vector direction drills: τ, L, and dL
Predict precession direction in top/gyro setups
Conceptual questions about “fast vs slow” spin
Identify assumptions behind steady-precession ideas
Exam-style qualitative gyroscope sets