Chapter 11, Problem 31P

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 ω_p=τ/I, where τ 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 × 10⁴ yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession.

Figure P11.31 A precessing angular momentum vector sweeps out a cone in space.