Editing Angular momentum (section)

== Examples ==
The trivial case of the angular momentum <math>L</math> of a body in an orbit is given by
<math display="block">L = 2 \pi M f r^2</math>
where <math>M</math> is the [[mass]] of the orbiting object, <math>f</math> is the orbit's [[frequency]] and <math>r</math> is the orbit's radius.

The angular momentum <math>L</math> of a uniform rigid sphere rotating around its axis, instead, is given by
<math display="block">L = \frac{4}{5} \pi M f r^2 </math>
where <math>M</math> is the sphere's mass, <math>f</math> is the frequency of rotation and <math>r</math> is the sphere's radius.

Thus, for example, the orbital angular momentum of the [[Earth]] with respect to the Sun is about 2.66 × 10<sup>40</sup> kg⋅m<sup>2</sup>⋅s<sup>−1</sup>, while its rotational angular momentum is about 7.05 × 10<sup>33</sup> kg⋅m<sup>2</sup>⋅s<sup>−1</sup>.

In the case of a uniform rigid sphere rotating around its axis, if, instead of its mass, its [[density]] is known, the angular momentum <math>L</math> is given by
<math display="block">L = \frac{16}{15} \pi^2 \rho f r^5</math>
where <math>\rho</math> is the sphere's [[density]], <math>f</math> is the frequency of rotation and <math>r</math> is the sphere's radius.

In the simplest case of a spinning disk, the angular momentum <math>L</math> is given by<ref name="hyperphysics">
{{cite web
 | url = http://hyperphysics.phy-astr.gsu.edu/hbase/tdisc.html
 | title = Moment of Inertia: Thin Disk
 | author = Department of Physics and Astronomy, Georgia State University
 | website = HyperPhysics
 | access-date = 17 March 2023
}}</ref>
<math display="block">L = \pi M f r^2</math>
where <math>M</math> is the disk's mass, <math>f</math> is the frequency of rotation and <math>r</math> is the disk's radius.

If instead the disk rotates about its diameter (e.g. coin toss), its angular momentum <math>L</math> is given by<ref name="hyperphysics" />
<math display="block">L = \frac{1}{2} \pi M f r^2</math>