Serway & Jewett — Angular Momentum: Problem 31

The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure P11.31. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by \(\omega_p = \tau/L\), where \(\tau\) 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 precesses about the perpendicular to its orbital plane with a period of \(2.58 \times 10^4 \text{ yr}\). Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession.