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Precession of a gyroscope
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A torque on a spinning wheel turns its axis sideways.
Ω = τ/LA torque from gravity on a spinning gyroscope changes the direction of L, so the axis sweeps round at Ω = τ/L = mgr/(Iω). The faster the spin, the slower the precession.
A spinning top at an angle doesn't fall at once.
Precession is perpendicular to the applied torque.
In more detail
A spinning gyroscope precesses when a torque is applied perpendicular to its spin axis. The axis rotates slowly around a vertical direction, rather than tipping over.
Real-world uses
- Gyroscopes in aircraft and ships stabilise orientation.
- Precession of the Earth's axis causes the slow shift in the pole star.
- A bicycle wheel held by one end of its axle slowly turns in a horizontal circle, which is precession under gravity.
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Frequently asked questions
Why doesn't a gyroscope fall over?
Because the torque from gravity changes the angular momentum direction, causing precession instead of falling.
How fast does it precess?
The precession rate is the torque divided by the angular momentum.
Why does the spinning wheel not fall over?
The weight produces a torque that changes the direction of the angular momentum, causing precession rather than falling.
Related topics in Rotational Motion
Conservation of angular momentum · Spinning skater and diver · Collisions in rotation · Nutation · Rotation of the Earth · Tops and bicycles