How Is the Angular Momentum of Earth Calculated?

AI Thread Summary
The discussion focuses on calculating the angular momentum of Earth using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia for a uniform sphere is given by I = (2/5)Mr^2, with Earth’s mass and radius provided. The angular velocity is calculated using ω = 2π/T, where T is the rotation period. The initial calculation yields an angular momentum of 1.958 X 10^31, which is significantly lower than the expected value of 7.1 X 10^33. The discrepancy suggests a potential error in the calculation of either the moment of inertia or the angular velocity.
sammythesp3rmy
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Homework Statement


Determine the angular momentum of the Earth about its rotation axis (assume the Earth is a uniform sphere).


Homework Equations


L = Iω
I = (2/5)Mr^2
ω = 2\pi/T


The Attempt at a Solution


I = (2/5)(6.0 X 10^24 kg)(6.4 X 10^6m)^2
ω = 1.992 X 10^-7 rad/sec

L = (2/5)(6.0 X 10^24 kg)(6.4 X 10^6m)^2 * (1.992 X 10^-7 rad/sec)
What I get from this is 1.958 X 10^31 and the answer is supposed to be 7.1 X 10^33. where did I go wrong? Thank you
 
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