Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

3.11: Torque and Rate of Change of Angular Momentum

( \newcommand{\kernel}{\mathrm{null}\,}\)

Theorem:

The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system.

Thus:

L=iri×pi

˙L=i˙ri×˙pi

But the first term is zero, because ˙r and pi are parallel.

Also

˙ri=Fi+Fij

˙Li=iri×(ri+jFij)=iri×Fi+iri×jFii

iri×Fi+iri×jFii

But ijFij=0 by Newton’s third law of motion, and so ijri×Fij=0.

Also iri×Fi=τ, and so we arrive at

˙L=τ

which was to be demonstrated.

Corollary: Law of Conservation of Angular Momentum

If the sum of the external torques on a system is zero, the angular momentum is constant.


This page titled 3.11: Torque and Rate of Change of Angular Momentum is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?