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| Conservation of Angular Momentum |
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| We already know two powerful conservation laws, namely, the conservation of energy and the conservation of linear momentum. Let us study another conservation law, namely the law of conservation of angular momentum. |
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| Torque is written in terms of angular momentum as |
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| If no net external torque acts on the system then, |
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i.e., if the net external torque acting on a system is zero, the angular
momentum
of the system remains constant, no matter what changes take place within the system. |
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| Next, we consider a rigid body rotating about an axis AB. Let the angular velocity of the body be w. Consider the ith particle going in a circle of radius ri, with its plane perpendicular to AB. The linear velocity of this particle at this instant is vi = ri w. The angular momentum of this particle about AB: |
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| The angular momentum of the whole body about AB is the sum of their components i.e., |
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| For a rigid body rotating about a fixed axis, L = Iw |
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| (a) The student has a relatively large rotational inertia about the rotation axis and a relatively small angular speed. (b) By decreasing his rotational inertia, the student automatically increases his angular speed. The angular momentum
of the rotating system remains unchanged. |
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| So, if the total external torque on the system is zero, its angular momentum remains constant. This is known as the principle of conservation of angular momentum. |
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