Physics XI Content
LAW OF CONSERVATION OF ANGULAR MOMENTUM
LAW OF CONSERVATION OF ANGULAR MOMENTUM | ||
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THE Law of Conservation of Angular Momentum STATES THAT: | ||
“When the net external torque acting on a system about a given axis is zero, the total angular momentum of the system about that axis remains constant.” | ||
Mathematically, | ||
If then = constant | ||
Proof | ||
According to the second law of motion net force acting on a body is equal to its rate of change of linear momentum. i.e. | ||
Taking vector product of on both side if above expression | ||
. | ||
But is the torque acting on the body | ||
… (i) | ||
Angular momentum is defined as: | ||
= x | ||
Differentiating both sides with respect to “t“ | ||
Which is the required equation. This expression states that the torque acting on a particle is the time rate of change of its angular momentum. If the net external torque on the particle is zero, then, | ||
OR | ||
Integrating both sides | ||
Thus the angular momentum of a particle is conserved if and only if the net external torque acting on a particle is zero. Search tag: theĀ law of conservation of angular momentum |