# Conservation of Angular Momentum

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The conservation of angular momentum is a fundamental concept of physics along with other conservation laws such as those of energy and linear momentum. It states that the angular momentum of a system remains constant unless changed through an action of external forces.

In Newtonian mechanics, the angular momentum of a point mass about a point is defined as  where  is the position vector of the point mass with respect to the point of reference and  is the linear momentum vector of the point mass.

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. This can be represented as:



where

 is the total angular momentum of the system
 is the angular momentum of the ith particle

## Proof of conservation

The derivative of angular momentum with respect to time is equal to the sum of the external moments (or torque ) applied to the system. Differentiating angular momentum gives:



For a constant radius, the second term is zero. Hence  From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.