Isaac Newton first published his three laws of motion in 1687 in his monumental Mathematical Principles of Natural Philosophy. In these three simple laws, Newton sums up everything there is to know about dynamics. This achievement is just one of the many reasons why he is considered one of the greatest physicists in history.
While a multiple-choice exam can’t ask you to write down each law in turn, there is a good chance you will encounter a problem where you are asked to choose which of Newton’s laws best explains a given physical process. You will also be expected to make simple calculations based on your knowledge of these laws. But by far the most important reason for mastering Newton’s laws is that, without them, thinking about dynamics is impossible. For that reason, we will dwell at some length on describing how these laws work qualitatively.
Newton’s First Law
Newton’s First Law describes how forces relate to motion:
An object at rest remains at rest, unless acted upon by a net force. An object in motion remains in motion, unless acted upon by a net force.
A soccer ball standing still on the grass does not move until someone kicks it. An ice hockey puck will continue to move with the same velocity until it hits the boards, or someone else hits it. Any change in the velocity of an object is evidence of a net force acting on that object. A world without forces would be much like the images we see of the insides of spaceships, where astronauts, pens, and food float eerily about.
Remember, since velocity is a vector quantity, a change in velocity can be a change either in the magnitude or the direction of the velocity vector. A moving object upon which no net force is acting doesn’t just maintain a constant speed—it also moves in a straight line.
But what does Newton mean by a net force? The net force is the sum of the forces acting on a body. Newton is careful to use the phrase “net force,” because an object at rest will stay at rest if acted upon by forces with a sum of zero. Likewise, an object in motion will retain a constant velocity if acted upon by forces with a sum of zero.
Consider our previous example of you and your evil roommate pushing with equal but opposite forces on a box. Clearly, force is being applied to the box, but the two forces on the box cancel each other out exactly: F + –F = 0. Thus the net force on the box is zero, and the box does not move.
Yet if your other, good roommate comes along and pushes alongside you with a force R, then the tie will be broken and the box will move. The net force is equal to:
Note that the acceleration, a, and the velocity of the box, v, is in the same direction as the net force.
Inertia
The First Law is sometimes called the law of inertia. We define inertia as the tendency of an object to remain at a constant velocity, or its resistance to being accelerated. Inertia is a fundamental property of all matter and is important to the definition of mass.
