State and prove the conservation of angular momentum.

Law of conservation of angular momentum states that the angular momentum of a rotating system about an axis remains constant in absence of any external torque.

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The law of conservation of momentum states that the total momentum of an isolated system with no external forces is conserved. When physicists say something is conserved they mean that the total amount remains constant. It can neither increase nor decrease.

The surface area of a triangle is proportional to the product of the base and the height. Here the base of each triangle is r, the radial distance, and the height is r·Δθ (where Δθ is the angle that is swept out during the time interval Δt)

Dividing the area by the interval of time gives the amount of area that is swept out per unit of time.

frac{Delta A}{Delta t} cong r^2 frac{Delta theta}{Delta t}

In the limit of Δt going to infinitisimal the expression for the conserved quantity is proportional to the following expression:

frac{dA}{dt} cong r^2 frac{dtheta}{dt} = r^2 omega

Where ω is the angular velocity.

So we have the following conserved quantity: r2ω

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