Question

Suppose that the Earth and Moon became tidally locked to each other with a period of...

Suppose that the Earth and Moon became tidally locked to each other with a period of 47 days and an Earth-Moon distance of 550,000 km. What would the total rotational energy of the Earth-Moon system be about its center of mass?
A. 9.7 x 10^25 J
B. 7.2 x 10^35 J
C. 2.0 x 10^38 J
D. 2.7 x 10^28 J
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Answer #1

w = angular speed = 2\pi/T = 2 x 3.14 / (47 x 24 x 3600) = 1.55 x 10-6 rad/s

I = total moment of inertia of moon around earth = Mmr2 = (7.35 x 1022) (550000,000)2 = 2.22 x 1040

rotational kinetic energy is given as

RKE = (0.5) I w2 = (0.5) (4.58 x 1041 ) (1.55 x 10-6 )2 = 2.7 x 1028

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