Interactive gyroscope simulator showing angular momentum, torque and precession. Spin up the rotor to see how L = Iω resists tilting — and when gravity applies torque, the gyroscope precesses instead of falling.
A spinning gyroscope resists changes to its orientation because angular momentum L is a conserved vector. Gravity creates a torque τ = r × mg perpendicular to L, causing the spin axis to precess at rate Ω = τ/L rather than topple.
Increase the spin speed and observe how the gyroscope holds steady. Reduce spin to see it wobble and eventually topple. The vectors L, τ, and Ω are drawn live to show their perpendicular relationships.
Gyroscopic precession explains why a thrown boomerang returns, why a bicycle stays upright at speed, and how spacecraft attitude control uses reaction wheels — all based on conservation of angular momentum.
This is a real 3D rigid-body gyroscope rendered with Three.js. A spinning rotor sits on a gimballed axle pivoted at one end of a stand; gravity pulls on its centre of mass and applies a torque about the pivot. Instead of toppling, the spin axis sweeps around the vertical — precession — while bobbing slightly up and down — nutation. The simulation integrates the heavy-top equations each frame, drawing the angular-momentum vector L, the torque vector τ, and a trail traced by the axis tip so you can orbit the camera and inspect the motion from any angle.
The physics follows from L = Iω and dL/dt = τ. Because gravity's torque τ = r × mg is perpendicular to the spin angular momentum, it rotates L sideways rather than speeding the fall, giving a steady precession rate Ω = mgr/(Iω). This conserved-angular-momentum behaviour stabilises spinning tops and bicycles, steadies spacecraft via reaction wheels and control-moment gyros, makes a thrown boomerang curve back, and drives the slow ~26,000-year precession of Earth's own rotation axis.
What is gyroscopic precession?
Precession is the slow circular sweep of a spinning gyroscope's axis around the vertical. When gravity applies a sideways torque, conserved angular momentum makes the spin axis rotate around instead of simply falling over.
Why doesn't the spinning gyroscope just fall down?
Gravity's torque acts perpendicular to the spin angular momentum L. Per dL/dt = τ, this changes the direction of L rather than adding downward motion, so the axis turns sideways (precesses) and the gyroscope stays up while it spins fast enough.
How is the precession rate calculated?
For a steadily precessing gyroscope it is Ω = mgr/(Iω), where m is mass, g gravity, r the pivot-to-centre-of-mass distance, I the moment of inertia, and ω the spin rate. Faster spin or larger I gives a slower precession.
Nutation is a small up-and-down nodding of the spin axis superimposed on the smooth precession. It appears as little looping cusps in the tip trail and is excited whenever the gyroscope is disturbed, for example by the "Give it a nudge" button.
Faster spin gives a larger angular momentum L = Iω. A bigger L resists the same gravitational torque more strongly, producing slower precession and a steadier, more upright axis that is harder to tip over.
With little or no spin there is almost no angular momentum to redirect the torque, so gravity simply topples the rotor. The "No spin (falls)" preset demonstrates this — the axle leans over and drops instead of precessing.
The yellow arrow is the angular-momentum vector L pointing along the spin axis; its length grows with spin. The red arrow is the gravitational torque τ, drawn horizontally and perpendicular to L, showing the direction in which L is pushed.
Partly. The spinning wheels add gyroscopic stability, and when a moving bike leans, gyroscopic and steering effects produce a corrective turn. Rider steering and trail geometry also matter, but conserved angular momentum is a key ingredient.
Satellites and telescopes use reaction wheels and control-moment gyroscopes to point and stabilise without expending fuel. Spinning these internal rotors exchanges angular momentum with the spacecraft body to rotate or hold its orientation.
Effectively yes. The Earth spins like a giant top, and the gravitational pull of the Sun and Moon on its equatorial bulge applies a torque that makes its rotation axis precess once roughly every 26,000 years — the precession of the equinoxes.