Angular momentum is a measure of the momentum of an object around an axis.

Linear momentum (**p**) is defined as the mass (**m**)
of an object multiplied by the velocity (**v**) of that object:

p = m*v.

With a bit of a simplification, angular momentum (**L**)
is defined as the distance of the object from a rotation axis multiplied
by the linear momentum:

This equation works for a single particle moving around a central point, for example a planet orbiting around the Sun or a rock tied onto a string that is swung in a circle. The mass is that of the planet, the velocity is the planet's orbital velocity, the distance can be taken as the semi-major axis of the orbit. (More accurately, the velocity and distance from the Sun both change as the planet moves in an elliptical orbit, but the product of the velocity times the distance stays constant, so we can pick any one point in the orbit and calculateL = r*porL = mvr.

wherev = 2*pi*R/T_{orb}

For a rigid body rotating on an axis (e.g., the Earth spinning), the angular momentum is the product of theL,_{orb}= M*(2*pi*R/T_{orb})*R= MR^{2}* 2*pi/T_{orb}

and for a rigid, spherical body,L,_{rot}= I*w

whereI = 0.4MR,^{2}

wherew = 2*pi / T,_{rot}

Example 1: The rotational angular momentum of the Earth isL._{rot}= 0.4 MR^{2 }* 2*pi / T_{rot}= 0.8*pi * MR^{2 }/ T_{rot}

Example 2: The orbital angular momentum of the Earth isL_{rot}= 0.8*pi * MR^{2 }/ T_{rot}L_{rot}= 0.8 * 3.14 * (5.98 x 10^{24}kg)(6.37 x 10^{6}m)^{2 }/ (8.64 x 10^{4 }s)L_{rot}= 7.1 x 10^{33}kg m^{2 }s^{-1}

Clearly, most of the Earth's angular momentum is in its orbit, not its rotation.L_{orb}= MR^{2}* 2*pi/T_{orb}L_{orb}= 2 * 3.14 *(5.98 x 10^{24}kg)(1.496 x 10^{11}m)^{2}/(3.15 x 10^{7 }s)L_{orb}= 2.7 x 10^{40}kg m^{2 }s^{-1}