The angular momentum vector of a precessing gyroscope sweeps out a cone as shown

Question

The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in the figure below. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by T/L, where s the magnitude of the orque on the gyroscope and L s the magnitude of its angular momentum n the motion called precession of the equino es the Earth sa s of rtation recesses aboutthe perpendicular to its orbital plane with a period of 2.58 x 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. N·m P L

Explanation / Answer

I=(2 / 5) M R^2 = (2 / 5) (5.98 x 10^24) (6.37 x 10^6)^2 = 9.70599 x 10^37

L = I = (9.70599x10^37)(2/3600/24) = 7.05840x10^33

= p L = [(2)/(2.58x10^4)/365.25/24/3600](7.0584...

= [(2 ) (7.05840) (10^29) ] / [ (2.58) (365.25) (24) (3600)]

= 5.44706 x 10^22= 5.45 x10^22 N-m

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