A fast-spinning gyroscope doesn't fall — it
precesses. Gravity's torque
τ = r×mg rotates the angular momentum vector,
making the spin axis sweep a cone at rate
Ω = mgr / (I·ω). Slow the spin and watch precession
speed up.
Spin ω: 20.0 rad/s
Precession Ω: 0.00 rad/s
Period T: —
L = Iω: —
τ = mgr·sinθ: —
🔭 Physics of Precession
When gravity pulls the gyroscope's centre of mass downward, it
exerts a horizontal torque τ = r × F perpendicular to
both the spin axis and vertical. Instead of falling, angular
momentum changes direction: dL/dt = τ, so the
spin axis sweeps a cone — a phenomenon called
steady precession.
Ω_prec = mgr·sinθ / (I·ω·sinθ) = mgr / (I·ω)
Key insight: precession rate Ω is
inversely proportional
to spin ω — a slower gyroscope precesses faster. This is why
well-thrown tops stay upright, and explains the 26,000-year wobble
of Earth's axis.
🌀 Gyroscope Precession
About this simulation
A spinning gyroscope tilted away from vertical does not topple over — instead its
spin axis slowly sweeps a cone, a motion called precession. The same physics
keeps spinning tops and bicycle wheels upright, stabilises spacecraft and satellites,
and drives the 26,000-year wobble of Earth's rotation axis. It is one of the most
counter-intuitive results in classical mechanics: pushing on a spinning object makes
it move sideways, not in the direction you pushed.
How it works
Gravity pulls down on the centre of mass, creating a torque about the pivot.
That torque is perpendicular to the angular momentum vector L of the spinning disk.
Because dL/dt = τ, the torque changes L's direction rather than its size.
The spin axis therefore rotates steadily, tracing a cone around the vertical.
Key equations
Omega = m·g·r / (I·omega) — precession rate Omega, where m is mass, g is
gravity, r is the distance from pivot to centre of mass, I is the moment of inertia, and
omega is the spin rate. Note that the tilt angle cancels out, and slower spin gives faster precession.
Controls
Spin rate ω — how fast the disk spins; lower ω makes precession visibly faster.
Tilt angle θ — lean of the axis from vertical.
CM distance r — pivot-to-centre-of-mass distance; larger r increases the torque.
Speed — time-scaling of the whole animation.
Presets, Pause, Vectors, Trace — load scenarios, freeze, show force arrows, draw the tip path.
Did you know?
The precession of Earth's axis means the "North Star" changes over millennia — around
3000 BC the pole star was Thuban, today it is Polaris, and in roughly 12,000 years it
will be the bright star Vega.