Editing Newton's laws of motion (section)

===Rotational analogues of Newton's laws===
When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the [[moment of inertia]], the counterpart of momentum is [[angular momentum]], and the counterpart of force is [[torque]].

Angular momentum is calculated with respect to a reference point.<ref>{{Cite journal |last1=Close |first1=Hunter G. |last2=Heron |first2=Paula R. L. |date=October 2011 |title=Student understanding of the angular momentum of classical particles |url=http://aapt.scitation.org/doi/10.1119/1.3579141 |journal=[[American Journal of Physics]] |language=en |volume=79 |issue=10 |pages=1068–1078 |doi=10.1119/1.3579141 |bibcode=2011AmJPh..79.1068C |issn=0002-9505}}</ref> If the displacement vector from a reference point to a body is <math>\mathbf{r}</math> and the body has momentum <math>\mathbf{p}</math>, then the body's angular momentum with respect to that point is, using the vector [[cross product]], <math display="block">\mathbf{L} = \mathbf{r} \times \mathbf{p}.</math> Taking the time derivative of the angular momentum gives <math display="block"> \frac{d\mathbf{L}}{dt} = \left(\frac{d\mathbf{r}}{dt}\right) \times \mathbf{p} + \mathbf{r} \times \frac{d\mathbf{p}}{dt} = \mathbf{v} \times m\mathbf{v} +  \mathbf{r} \times \mathbf{F}.</math> The first term vanishes because <math>\mathbf{v}</math> and <math>m\mathbf{v}</math> point in the same direction. The remaining term is the torque, <math display="block">\mathbf{\tau} = \mathbf{r} \times \mathbf{F}.</math> When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant.<ref name=":2" />{{Rp|pages=14-15}} The torque can vanish even when the force is non-zero, if the body is located at the reference point (<math>\mathbf{r} = 0</math>) or if the force <math>\mathbf{F}</math> and the displacement vector <math>\mathbf{r}</math> are directed along the same line.

The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points. This provides a means to characterize a body's rotation about an axis, by adding up the angular momenta of its individual pieces. The result depends on the chosen axis, the shape of the body, and the rate of rotation.<ref name=":2" />{{Rp|page=28}}