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The principle of angular momentum can be applied to a system of particles by summing the angular momentum of each particle about the same point.

The principle of angular momentum can be applied to a system of particles by summing the angular momentum of each particle about the same point.

The [[derivative]] of angular momentum with respect to time is equal to the sum of the external moments applied to the system. This relation is shown by the equation <math>\vec {\dot H} = \vec r \times \vec F</math> From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.

The [[derivative]] of angular momentum with respect to time is equal to the sum of the external moments (or torque <math>\vec {\tau}</math>) applied to the system. Differentiating angular momentum gives:

 

 

For a constant radius, the second term is zero. Hence <math>\vec {\tau}= \vec r \times \vec F</math> From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.

[[Category:Physics]]

[[Category:Physics]]