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 torque then L Constant = 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.
net force
Taking vector product of r on both side if above expression
vector product of r.
But vector product of r is the torque acting on the body
torque acting on body… (i)
Angular momentum is defined as:
angular momentum = r x p
Differentiating both sides with respect to “t
differentiating with t
differentiating with t
required equation
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,
angular momentum
OR
dL
Integrating both sides
integrating
Thus the angular momentum of a particle is conserved if and only if the net external torque acting on a particle is zero.

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