Linear momentum of a particle is a physical quantity with state of motion and defined as the product of mass and velocity (not speed)
That is, p = mv
Though the word linear is not commonly employed but it is sometimes used to distinguish it from angular momentum.
Units of linear momentum are kgms-1 or N-s
Linear momentum depends upon the frame of reference for example, the linear momentum of a body at rest in a moving train, is zero relative to a person sitting in the train while it is not zero for a person standing on the ground. Two bodies of same mass and moving with same speed will have different momentum unless their directions of motion are same.
For a body or a particle p = mc, so the linear momentum will change if mass or velocity or both change.
If m = constant then p ∝ v, that is, if different bodies have same mass, the momentum will be arrest of the fastest moving body
If v = constant then p ∝ m, that is, if different bodies are moving with same velocity then momentum is largest of the heaviest body.
If p = constant then v ∝1/m, that is different bodies have same momentum the lightest body will have greatest velocity.
P2 / 2m = (KE) ∴p = √2 (KE) m
If p = constant kinetic enercy ∝ 1/m, that is, if different bodies have same momentum, kinetic enercy will be maximum for lightest body.
If kinetic enercy = constant then p ∝ √m that is, different bodies have same kinetic enercy, then heaviest body will possess maximum momentum
If m = constant then p ∝ √K that is,, if different bodies have same mass, the body having largest KE will have maximum momentum.
Since F = dp / dt, the slope of p – t curve will yield force and the area under F – t curve will give the change in momentum.
P = h /λ for particle wave and p = E / c for photons.
Law of conservation of linear momentum in an isolated system (if no external force acts) of constant mass (closed) the total momentum of the system remains constant (with time). According to this law ∑pi = constant.
This equation clarified that linear momentum of various particles may change but their sum remains unchanged. Law of conservation of momentum is independent of frame of reference though it depends on the frame of reference. Conservation of linear momentum is equivalent to Newton’s third law of motion
p1 + p2 = constant
Differentiating with respect to time
dp1 / dt + dp2 / dt = O or F1 + F1 = O F2 + F1
that is for every action there is an equal and opposite reaction.
Law of conservation of momentum is universal, that is, it applies to both microscopic and macroscopic particles. It holds good even in atomic and unclear physics where classical physics fails.
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