A rapidly spinning top does not simply topple over when tilted, even though gravity pulls down on its center of mass and clearly exerts a torque about the pivot point. Instead its spin axis sweeps out a slow, steady cone — a motion called precession. This is one of the more counter-intuitive results in classical mechanics: applying a torque perpendicular to a large angular momentum vector rotates that vector sideways instead of tipping it in the direction of the torque.
L = Iω directed along its symmetry axis.τ = r × mg, horizontal and perpendicular to the axis.dL/dt = τ, means L changes in the direction of τ — sideways, not downward — so the axis sweeps around in a cone.Ω ≈ τ / (I·ω·sinθ) = mgr / (Iω): faster spin or lower torque means slower, tighter precession.The same physics keeps a bicycle wheel from falling when spun on a string, makes Earth's axis slowly trace a 26,000-year precession cycle due to solar and lunar torque on its equatorial bulge, and is exploited in mechanical gyrocompasses used for navigation before GPS.
A spinning top tilted from vertical does not fall — gravitational torque acting on a fast-spinning body redirects its angular momentum sideways, tracing a slow cone instead of collapsing straight down.
Precession rate Ω is inversely proportional to spin rate ω: Ω ≈ mgr / (Iω). Faster spin means slower, tighter precession; more mass, more tilt-arm, or stronger gravity all speed it up.
Adjust spin rate, tilt angle, mass, and gravity to see how each changes the precession cone. The blue arrow shows the instantaneous torque direction; the yellow trace traces the axis tip's circular path.
Earth's own axis precesses this way over a ~26,000-year cycle due to solar and lunar torque on its equatorial bulge — the same physics as a spinning top, just vastly slower.