Gyroscope and precession — why a spinning top doesn't fall

What just happened?

You spun the top up, and its axis stopped dropping and only slowly traces a circle (precession). The faster it spins, the more stable the upright position.

Angular momentum of a rigid body:

— angular momentum is directly proportional to the spin rate. $I$ — moment of inertia, $\omega$ — angular velocity of the spin. A large $L$ is a vector that "defends" its direction.

Why does the top precess instead of falling?

Gravity provides a torque $mgr$, which does not topple the axis but rotates it around the vertical at a rate:

The larger $\omega$ (and therefore $L$), the slower the precession and the more stable the upright position. For small $\omega$ the precession is fast and the axis clearly drops.

Why you need this for the exam:

The relations $L = I\omega$ and $\Omega = mgr/(I\omega)$ explain the stability of a bicycle wheel, a phone gyroscope, or the Earth. Key idea: large angular momentum = small precession = axis direction "frozen".

Remember: a fast spin gives a large angular momentum $L = I\omega$, which resists any change in direction — so the top stays upright and precesses more slowly the faster it spins.