Conservation of Angular Momentum for the Special Case in which no
Angular Momentum is Transferred to or from the System from Outside the
System
In any physical process involving an object or a system of objects free to rotate about an axis, as
long as there are no external torques exerted on the system of objects, the total angular
momentum of that system of objects remains the same throughout the process.
Examples
The application of the conservation of angular momentum in solving physics problems for cases
involving no transfer of angular momentum to or from the system from outside the system (no
external torque) is very similar to the application of the conservation of energy and to the
application of the conservation of momentum. One selects two instants in time, defines the
earlier one as the before instant and the later one as the after instant, and makes corresponding
sketches of the object or objects in the system. Then one writes
L = L′ (5-2)
meaning "the angular momentum in the before picture equals the angular momentum in the after
picture." Next, one replaces each L with what it is in terms of the moments of inertia and angular
velocities in the problem and solves the resulting algebraic equation for whatever is sought.
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