What are laws in physics? Many times a precise definition of something in physics is not available but yet there exist some rough definitions that guide us through. I need the same rough (if not precise) definition of physical laws. The reason being that we would consider $\mathbf a= \frac {d \mathbf v}{dt}$ as a mere definition but $\mathbf F =m \mathbf a$ as a law (as it is called as Newton's second law of motion). But to me it seem to be more inclined towards being as definitions rather than laws. I mean contrasting Newton's laws of motion to the law of conservation of energy (momentum, etc) it seem to be an attempt to define forces ( though I might be wrong at this (but I don't know reason for such)).


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*So what is the definition of a physical law that can encapsulated it's entirety?

 A: As pointed out by Safesphere, the physical laws that rule the world are expressed at a higher and more general level of (mathematical) abstraction which underlie Newton's laws. We can then derive Newton's laws from them as needed to solve everyday problems in real-world dynamics. 
These more general relationships are generically called symmetries; if you know what they are for a given system then you can in a sense solve the problem once by working with those symmetry equations and apply the general form of the solution to any of an entire class of related problems, making them easier to solve. This is a very powerful and general technique which is why physicists use it. 
As pointed out by dmckee, this question has been asked and answered before but the reason I am answering it here is in doing so I get the chance to test my own understanding of the topic. If I get it wrong, then the experts here will point out my errors and I then learn something new. 
Please write back if you are interested in examples of symmetries and I'll furnish you with some.  
A: When one studies mathematics, one knows that a mathematical theory  starts from axioms and then mathematics is used to prove theorems. When axioms change, the theory changes. A good example is Euclidean Geometry versus spherical geometry. Also in mathematics, a theorem may be used as an axiom, and the original axiom proven as a theorem.
Physics theories use mathematics as a tool to describe the natural world. But the mathematics of differential equations used extensively in physics, have an infinity of solutions and forms. It is necessary to use new "axioms" in order to pick up those solutions that are relevant to measurements and observations. These physics "axioms" are called "laws" "postulates" "principles" and are extracted from many observations and measurements so that the physics theory not only fits the data,but, very important, predicts new situations. (Just fitting data makes a mathematical map). At the same time there are at the level of axioms statements identifying the objects measured, mass, charge, (plus a lot of quantum numbers for particles) 
Take $F=ma$ for example. It is a law, because when using it axiomatically ( together with the other two) Newtonian mechanics theory works beautifully, from predicting the  planetary system, to trajectories of rockets , to stability of buildings etc.
The concept of force and mass  existed in everyday language, because of the need to quantify products  and the need to quantify effort, both everyday manifestations. The brilliant use though of the relation between acceleration , mass, and force brought the existence  a complete and self consistent theoretical model for describing nature.
