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Spinning Top

In fact, the precession of wheel described above is not confined to spinning of the wheel about horizontal axis. A gyroscope set with its axis at an angle θ to the vertical also precesses about Z-axis thus sweeping a cone. This is best illustrated by a spinning top.

The spin angular momentum is along Z’-axis, making angle θ with vertical (Z-axis). Weight Mg acts at C downwards, while torque due to weight about O is given by

where, l = OC, l sin θ is normal distance between O and line of force (Mg). Note that direction of τ is perpendicular to plane of paper and hence to L vector. L vector therefore precesses about Z-axis, with angular velocity Ω such that

Note that dL = ( L sin θ) d Ø. Hence, we get

which is the same result as obtained earlier. Above results are true (exactly) only if ω >> Ω.

The tendency of a gyroscope not to fall down and maintain the direction of its spin-axis makes it a useful device with wide applications. It is thus used in ships and aeroplanes as an automatic stabilizer.

Earth itself is a spinning top. Its axis of spin (line joining North and South poles) precesses about the direction perpendicular to the ecliptic plane. (Ecliptic plane is the plane of revolution of earth around Sun.) It completes one cycle of precession in 27725 years.