An object at rest will stay at rest until an unbalanced force acts on the object.An object moving will stay at the same speed and direction until acted upon by an unbalanced force. That is the first law of motion.
If you jump up, for example, with a momentum of 100 kilogram x meter / second (this can be done by jumping up at a speed of 2 meters/second, if you have a mass of 50 kilograms), then the Earth will recoil by the same amount of momentum - in the opposite direction of course. This follows directly from Conservation of Momentum.
More or less. There is a law of conservation of angular momentum, according to which Earth can't gain or lose angular momentum on its own - if for example it loses angular momentum, it has to go somewhere. A meteor who falls into the Earth, or a rocket leaving the Earth can change Earth's angular momentum - but the total angular momentum (e.g., of the system meteor + Earth) is the same, before and after the impact.
This is an example of Newton's Third Law. It can also be explained - equivalently - via conservation of momentum.
Simply because physicists discovered that it is a product that is conserved. In collisions of two objects for example, if you add up the momentum before the collision the momentum will be the same after the collision. Note that momentum is not something that has a concrete reality. A rock sitting on the ground has zero momentum relative to us here on earth but has alot of momentum relative to someone on mars. It can not have zero momentum and alot of momentum at the same time, it depends on ones frame of reference. My point is that momentum is not at 'concrete" thing. Refer to the 'Conservation of linear momentum' in Wikipedia.org, "The World's Encyclopedia" *Check out related links*
The details depend on what you want to solve for. Quite often, in practice you would use the Law of Conservation of Momentum - just write an equation that states that the total momentum after a collision (for example) is the same as it was before the collision. This can often help you calculate things such as velocities.
Elastic collision.
No, there has not been a single violation of the law of conservation of momentum.
There are several laws of conservation; please clarify which one you mean. For example, there is the law of conservation of mass, of energy, of momentum, of rotational momentum, of electrical charge, and others.
the equal force applied by a wall when you push agaginst it
In an isolated system the total momentum of a system remains conserved. For example If you fire a bullet from Gun , bullet go forward with some linear momentum and in order to conserve the linear momentum the gun recoils
a series of dominos being knocked over one by one
For example, various conservation laws (conservation of mass, of energy, of momentum, of angular momentum, of electric charge), Newton's Second Law, the Universal Law of Gravitation, etc.
You mention conservation in general; there are several conservation laws, like conservation of energy, of linear momentum, of rotational momentum, of electrical charge, and others. This is originally based on experience - for example, no cases are known where the linear momentum is violated. However, these conservation laws (or many of them?) can be explained with Noether's Theorem. This is some very advanced math (for me, at least), but basically, it states that for every symmetry in nature, there is a corresponding conservation law. For example, the fact that the laws of physics are the same today as a year ago (they don't change over time) is related to the Law of Conservation of Energy; the Law of Conservation of Momentum is related to a symmetry with respect to position (the laws of nature are the same here as on the Moon), and the Law of Conservation of Rotational Momentum is related to a symmetry with respect to rotation (if you rotate an experimental apparatus, the results won't change).
The law of conservation of momentum is Newton's 3rd law' The vectors sum to zero: 0 = F1 + F2 = dp1/dt + dp2/dt = d(p1 + p2)/dt =0. Thus, p1 + p2 = a constant, thus, the conservation of momentum.
A "law of conservation" is a law, in physics, that states that some quantity doesn't change over time. There are several conservation laws; such as the law of conservation of mass, of energy, of momentum, of rotational momentum, of electric charge, of color charge, and several others more.
This is an example of Newton's Third Law. It can also be explained - equivalently - via conservation of momentum.
Linear momentum is mass times velocity. For a single point object, momentum is conserved, because the object will continue to move at a constant velocity. Nor will its mass change either. For a group of objects, too: When momentum is transferred, for example during a collision, any momentum lost by one object is gained by another. The total momentum remains constant.