The angular momentum vector of a processing gyroscope sweeps

The angular momentum vector of a processing gyroscope sweeps out a cone as shown in the figure below. The angular speed of the tip of the angular momentum vector, called its professional frequency, is given by omega_p = tow/L, where tow is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earth\'s axis of rotation processes about the perpendicular to its orbital plane with a period of 2.58 times 10^4 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession.

Solution

I = 2 / 5 * M R²

=2 / 5 * 5.98 * 10²⁴ * (6.37 * 10⁶)²

= 9.71 * 10³⁷

L = I w = 9.71 * 10³⁷ * ( 2 pi / 3600 / 24) = 7.06 x 10³³

T = w p L = [ (2 pi) / (2.58 * 10⁴) /365 / 24 / 3600] * 7.06 x 10³³

= 5.45 * 10²² N.m