alleryStart learning →Earth is treated as a uniform sphere of mass 5.979 x 10^24 kg and radius 6.376 x 10^6 m, turning once per day. What is its angular momentum?
A9.72 x 10^37 kg m^2/s
B7.07 x 10^33 kg m^2/s
C7.07 x 10^37 kg m^2/s
D2.39 x 10^24 kg m^2/s
Answer & Solution
Correct answer: B. 7.07 x 10^33 kg m^2/s
1. Angular momentum is L = I omega, and a sphere has I = two fifths M R squared.
2. Substituting, I = 0.4 (5.979 x 10^24 kg)(6.376 x 10^6 m) squared = 9.72 x 10^37 kg m^2.
3. One turn per day means omega = 2 pi rad per 8.64 x 10^4 s.
4. So omega = 7.27 x 10^-5 rad/s.
5. Then L = (9.72 x 10^37 kg m^2)(7.27 x 10^-5 rad/s) = 7.07 x 10^33 kg m^2/s.
6. Answering 9.72 x 10^37 quotes the moment of inertia and never multiplies by omega.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.5 Angular Momentum and Its Conservation_
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