# 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:

$\overline{){\mathbf{L}}{\mathbf{=}}{\mathbf{I}}{\mathbf{\omega }}}$

Moment of inertia of the earth is expressed as:

$\overline{){\mathbf{I}}{\mathbf{=}}{\mathbf{M}}{\mathbf{·}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Therefore,

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

Angular velocity:

ω = 2π/t

ω = 1.99 × 10-7 rad/s

95% (485 ratings) ###### 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.