Conservation of angular momentum
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Proof of the result (conservation of angular momentum)
Equations are omitted for technical reasons - download the original pdf
We now proceed to prove the main result - that in any collision, or closed system, angular momentum is conserved. Consider the collision of two particles P and P' of mass M and M' and velocities V and V' respectively. Let the collision be modelled by the collision of particles of no size at a distance r from a point O. [Diagram goes here - download the original to see it.] Let I = mr2 be the moment of inertia of P about any axis of rotation L through O. Let I' = m'r2 be the equivalent moment of inertia of P'. As a result of the collision P imparts an impulse, that is a change of momentum to P'. By the conservation of linear momentum P' imparts a change in momentum to P that is equal and opposite to this impulse. Thus [Equation goes here - download the original to see it.] multiplying both sides by r: [Equation goes here - download the original to see it.] Thus demonstrating conservation of angular momentum.
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Contents of
Conservation of angular momentum
1 Conservation of Angular Momentum
2 Proof of the result (conservation of angular momentum)
3 Rotational kinetic energy
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