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Conservation of Angular Momentum

Angular momentum, the rotational equivalent of linear momentum, is conserved in the absence of external rotational forces (torques).  This means that if there are no external torques, the total angular momentum at one instant in time has to equal the total angular momentum at another instant in time.  Like linear momentum, angular momentum is based on the product of mass and velocity but it also includes the product of the radius from the center of rotation (axis) to the radial center of mass. One possible version of this formula can be seen below. 

 Angular momentum equals m v r

Note: The capital letter "L" is often used to represent angular momentum  in place of .

The concept of conservation of angular momentum is illustrated the same way as we illustrate the conservation of linear momentum:

The total momentum before = The total momentum after.

Large Radius small velocity
image: small radius leads to higher velocity
Small velocity, Large Radius Large Velocity, small radius

Conservation of angular momentum allows ice skaters to spin faster or slower, cats to land on their feet, and divers to flip, twist, spiral and turn.  It also makes water circle the drain faster as it gets closer to the drain.  The skaters spin is illustrated above.