Section 1.3 Newtonian Mechanics
Many of the concepts behind Classical Physics are motivated by Newtonian Mechanics, which is derived from Newton’s three laws of motion. These laws provide a framework for determining how an object will move when acted upon (or not acted upon) by external forces. Newton’s three laws were first described in his Philosophiæ Naturalis Principia Mathematica, which is widely considered to be one of the most important works in the history of physics.
Newton’s first law, put simply, is that in the absence of external forces, an object at rest will stay at rest and an object in motion will stay in motion. Furthermore, without outside interference, an object in motion will travel at a constant speed in a straight line. In Principia, Newton defines inertia as the property of matter to preserve its current state and resist attempts to change it. Thus, the first law of motion establishes that all objects have the property of inertia and resist changes to their state of rest or motion.
The second law of motion is often abbreviated by the equation \(\sum \vec{F} = m\vec{a}. \) This equation tells us that the acceleration (\(\vec{a}\)) of an object is directly proportional to the net force (\(\sum \vec{F}\)) acting upon it and is inversely proportional to the mass (\(m\)) of the object. Mass can be thought of as a numerical measure of inertia, so the second law relates to the first law in that objects with a lot of mass, i.e. objects with a lot of inertia, require greater forces to accelerate. Furthermore, if we look at the case where there are no forces acting upon an object, i.e. \(\sum \vec{F}=0\text{,}\) we know that \(m\vec{a}=0\) as well. Since the mass of an object can never be \(0\text{,}\) when there are no forces acting upon an object, it must have an acceleration of \(0\text{.}\) In the absence of acceleration, an object at rest will stay at rest and an object in motion will continue to travel at a constant speed.
Newton’s third law states that when two objects interact, the force exerted by the first object on the second is equal in magnitude and opposite in direction to the force exerted by the second object on the first. Simply put, every action has an equal and opposite reaction.
The three laws of motion can be seen in the example of a rocket launching into space. As the thrusters begin to fire, the rocket does not immediately begin to move. Since the rocket begins at rest, its inertial properties resist changing to a state of motion, which showcases the first law. Once the rocket begins to lift off the ground, it appears to be moving upwards slowly. Since the rocket is very heavy, it has a lot of mass, and since acceleration is inversely proportional to mass by Newton’s second law, it thus accelerates slowly. The third law of motion can be seen in the fact that the rocket engines are pushing down, which causes the equal and opposite reaction of the rocket to move upwards.
