\n Newton's first law states that:\r\n
\"An object does not change its state of motion unless\r\n acted upon by an external force.\"\r\n \r\n
This means that an object which is at rest will continue to be at rest\r\n and a moving object will keep moving if no external force is applied on it.\r\n Mathematically, we can say that:\r\n $$\\textbf{F}_{net}=0 \\iff \\frac{d\\textbf{v}}{dt}=0$$\r\n The concept of inertia is very closely related to the first law. In fact\r\n sometimes the first law is called the Principle of Inertia\n
\n The Mathematical statements might not seem very intuitive. So let us look at some real\r\n life examples of the First Law and Inertia.\n
\r\n\n Newton's Second Law quantitatively defines Force but before we get there, lets first look\r\n at the qualitative definition of Force which we get from The First Law:\r\n
\"Force is that physical cause which changes the state of rest or motion of a body\" \r\n
This definition comes from the First Law. Now we will see the Second Law:\r\n
\"The rate of change of momentum of a body is directly proportional to the applied force and\r\n occurs in the same direction as the direction of the force applied.\" \r\n Mathematically,\r\n $$\\textbf{F}=\\frac{d\\textbf{p}}{dt}$$\r\n Using \\(\\textbf{p}=m\\textbf{v}\\) in the above equation,\r\n $$\\textbf{F}=m\\frac{d\\textbf{v}}{dt}+\\textbf{v}\\frac{dm}{dt}$$\r\n In most cases, mass of our system remains constant, so the above\r\n equation reduces to the famous \\(\\textbf{F}=m\\frac{d\\textbf{v}}{dt}=m\\textbf{a}\\)\n
\n There are however some cases where the mass of a system does not remain constant (like in a rocket\r\n which continuously uses up its fuel) and in such cases we cannot use \\(\\textbf{F}=m\\textbf{a}\\)\n
\r\n\n Newton's third law is pretty simple. It states that:\r\n
\"Every action has an equal and opposite reaction\"\r\n
Now lets see some examples to understand this:\n