Concept Of Linear Momentum and definition of Force

[physio]

I understood that Newton has introduced a concept called "Force" which is basically a cause for an effect i.e. if an object is in a state of rest and if applied a "force" then the object moves (change in velocity, ∴ accelerates) also if an object moves with a constant velocity and is disturbed then an acceleration is produced for the same reason as above. Thus a force is a cause and a change in velocity is an effect. This, based upon my understanding, is deduced from the law of inertia (given by Galileo and simply restated by Newton)!

What I don't follow is that:-
1) JUST WHAT IS THE CONCEPT OF LINEAR MOMENTUM?!

2) Why is momentum expressed as mass TIMES velocity?

3) How did Newton obtain the second law from the momentum concept?

Please can anyone give examples and explain the momentum concept?

 

[NascentOxygen]

Momentum is a property of motion that is conserved during interactions of free bodies. This fact allows us to calculate velocity vectors after colliding bodies separate, based on their masses and velocity vectors prior to collision^. During most such collisions kinetic energy is not conserved; so it's handy that momentun is.

^or viceversa

 

[jartsa]

I understood that Newton has introduced a concept called "Force" which is basically a cause for an effect i.e. if an object is in a state of rest and if applied a "force" then the object moves (change in velocity, ∴ accelerates) also if an object moves with a constant velocity and is disturbed then an acceleration is produced for the same reason as above. Thus a force is a cause and a change in velocity is an effect. This, based upon my understanding, is deduced from the law of inertia (given by Galileo and simply restated by Newton)!

I would say that a push is a cause of a velocity change. A pull works just as well.

What I don't follow is that:-
1) JUST WHAT IS THE CONCEPT OF LINEAR MOMENTUM?!

One thing that linear momentum is, is a number that describes a push. If you measure the duration of a push and the force of the push, and multiply those, you get the linear momentum.

2) Why is momentum expressed as mass TIMES velocity?

Mass times velocity is an useful number to know, we have named it momentum.

3) How did Newton obtain the second law from the momentum concept?

I have no idea