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Problem: Calculate the magnitude of the angular momentum of the Earth in a circular orbit around the sun. The Earth has mass 5.97×1024 kg , radius 6.38×106 m , and orbit radius 1.50×1011 m . The planet completes one rotation on its axis in 24 hours and one orbit in 365.3 days.Is it reasonable to model it as a particle?Calculate the magnitude of the angular momentum of the Earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere.

FREE Expert Solution

Angular momentum:

L=Iω

Moment of inertia of the earth is expressed as:

I=M·R2

Therefore, 

I = (5.97 × 1024)(1.50 × 1011)2 = 1.34 × 1047 kg•m2

Angular velocity:

ω = 2π/t

ω=(2π rad365days)(1day24h)(1h3600s)

ω = 1.99 × 10-7 rad/s

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Problem Details

Calculate the magnitude of the angular momentum of the Earth in a circular orbit around the sun. The Earth has mass 5.97×1024 kg , radius 6.38×106 m , and orbit radius 1.50×1011 m . The planet completes one rotation on its axis in 24 hours and one orbit in 365.3 days.

Is it reasonable to model it as a particle?

Calculate the magnitude of the angular momentum of the Earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere.

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