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Assuming the Earth is a uniform solid sphere with radius R and mass M, what is its angular momentum about its rotation axis if its period of rotation is T?

1. πMR³/T
2. MR²π/T
3. 2πMR²/5T
4. 4πMR²/5T

Correct answer: 4πMR²/5T

Solution

For a uniform solid sphere, I = (2/5)MR^2 and omega = 2pi/T. Angular momentum L = I*omega = (2/5)MR^2*(2pi/T) = 4 pi M R^2/(5T).

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