Law of conservation of Linear and Angular Momentum

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Law of Conservation of Linear and Angular Momentum 

The law of conservation of momentum implies,

Linear Momentum before colliding = Linear Momentum after colliding 

But from the definition of momentum from linear momentum Newton’s second law

rate of change of momentum equals force 

dP/dt = F

We know F=na

dP/dt = mdv/dt

Mass remains constant.

For a conserved quantity, the rate of change of momentum should be conserved.

dP/dt = 0 for momentum conserved

Since F=dP/dt

So dP/dt = 0 implies F=0.

Another definition:

The linear momentum of a particle is conserved if the total force that acts on the particle is zero.

 

If 5N force acts from left and 5 N force from right, momentum is conserved or the change in momentum is zero.

Another definition: 

The component of linear momentum of a particle is constant in a direction in which force vanishes. 

Momentum P has three components along x, y, and z. If the force along the c component is zero, the momentum along the x component is constant in time.

Law of Conservation of Angular Momentum

If the net torque acting on the body equals zero, the angular momentum of the body will be conserved in time.

Let N be the torque.

And L be the angular momentum.

If N=0, dL/dt=0 or L=constant in other words. 

For proofs see the images below.