Angular Momentum Conservation
The angular momentum of the particle O, moving in a central force F = Fr er, about the center of force is, by definition,
L = r × p
= v × m v + r × Fr er
= 0
Thus, the angular momentum of a particle moving in a central force is always conserved. This happens because central forces do not exert any torque on the particle about center of force:
The value of angular momentum is,
where n is the unit vector normal to the (r, θ) plane of motion. (We call the direction of n as Z-axis, i.e. n = k). Since the plane of motion remains fixed (decided by initial position and velocity vectors), n is a constant vector. Hence, L = constant implies,
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