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(In classical mechanics), the definition of momentum is $\vec{p}=m\vec{v}$. The reason this is a good definition is because it is useful. In particular, the momentum of a collection of particles that are not in an external potential is conserved. Conserved quantities make it possible to understand aspects of the behavior of a system without ...
Furthermore momentum is conserved $\Sigma m_{i}\vec{v_{i}}=const.$ Then you have the definition that force is the change of momentum with respect to time $\vec{F}=\dfrac{d(m\vec{v})}{dt}$. I've read the chapters concerning mechanics of Physics for scientists and engineers by Giancoli and the Feynman Lectures.
Classical mechanics is a very successful theory, and conservation of momentum is a law. Then comes classical electrodynamics with Maxwell's equations. It can be shown that the electromagnetic wave carries energy. Then using the law of conservations of momentum, the momentum carried by the electromagnetic wave can be derived, as shown here. I.e ...
Momentum: The resistance of an object to a change in its state of motion. That sounds like a fishy definition of momentum to me. A slightly better definition, at least at your level, is that momentum represents the "amount of motion" an object has. Granted, "amount of motion" is a very vague term, but it stands to reason that if "amount of ...
Momentum is the quantity needed to completely remove all movement from a rigid body or a point mass. Specifically, momentum is a vector quantity applied along an infinite line in space (the axis of percussion). An impulse (a short lived force) of equal and opposite magnitude and direction, but along the same line applied on a moving body will ...
Newton thought of momentum as "Quantity of motion" - as we can see in the translated version of 'Principia'. Particularly, he defined momentum in the following words: The quantity of motion is the measure of the same, arise from the velocity and quantity of matter conjointly. So yeah, that is the definition of momentum.
So we see that the quantity momentum naturally arises as the thing that is conserved under space-translation symmetry. But this notion of momentum extends much further than free particles. It can be applied to any Lagrangian with space-translation symmetry, with the conserved quantities that arise being given the label momentum.
$\begingroup$ Though the conclusion is correct in reality, where p=mv, the original question is based on F=ma being derived from the momentum definition of force, so this proof would be self-inconsistent, because if p=mv^2 leads to F=2vma, then F != ma, so the last step converting 2vma to 2vF is invalid. $\endgroup$
The component of momentum transverse (i.e. perpendicular) to the beam line. It's importance arises because momentum along the beamline may just be left over from the beam particles, while the transverse momentum is always associated with whatever physics happened at the vertex.
So the definition of angular momentum should be this: "Angular momentum is the product of the angular velocity of the body or system and its moment of inertia with respect to the rotation axis, and that is directed along the rotation axis".