Angular momentum:

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

Moment of inertia of the earth is expressed as:

$\overline{){\mathbf{I}}{\mathbf{=}}{\mathbf{M}}{\mathbf{\xb7}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Therefore,

I = (5.97 × 10^{24})(1.50 × 10^{11})^{2} = 1.34 × 10^{47} kg•m^{2}

Angular velocity:

ω = 2π/t

$\begin{array}{rcl}\mathbf{\omega}& \mathbf{=}& \mathbf{\left(}\frac{\mathbf{2}\mathbf{\pi}\mathbf{}\mathbf{r}\mathbf{a}\mathbf{d}}{\mathbf{365}\overline{)\mathbf{d}\mathbf{a}\mathbf{y}\mathbf{s}}}\mathbf{\right)}\mathbf{\left(}\frac{\mathbf{1}\overline{)\mathbf{d}\mathbf{a}\mathbf{y}}}{\mathbf{24}\overline{)\mathbf{h}}}\mathbf{\right)}\mathbf{\left(}\frac{\mathbf{1}\overline{)\mathbf{h}}}{\mathbf{3600}\mathbf{s}}\mathbf{\right)}\end{array}$

ω = 1.99 × 10^{-7} rad/s

Calculate the magnitude of the angular momentum of the Earth in a circular orbit around the sun. The Earth has mass 5.97×10^{24} kg , radius 6.38×10^{6} m , and orbit radius 1.50×10^{11} 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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What scientific concept do you need to know in order to solve this problem?

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