Newton’s First Law

Newton’s first law: If the total force acting on an object is zero, its center of mass continues in the same state of motion.

In other words, an object initially at rest is predicted to remain at rest if the total force acting on it is zero, and an object in motion remains in motion with the same velocity in the same direction. The converse of Newton’s first law is also true: if we observe an object moving with constant velocity along a straight line, then the total force on it must be zero. You may encounter the term “net force,” which is simply a synonym for total force.

What happens if the total force on an object is not zero? It accelerates. Numerical prediction of the resulting acceleration is the topic of Newton’s second law.

This is the first of Newton’s three laws of motion. It is not important to memorize which of Newton’s three laws are numbers one, two, and three. If a future physics teacher asks you something like, “Which of Newton’s laws are you thinking of?,” a perfectly acceptable answer is “The one about constant velocity when there is zero total force.” The concepts are more important than any specific formulation of them. Newton wrote in Latin, and I am not aware of any modern textbook that uses a verbatim translation of his statement of the laws of motion. Clear writing was not in vogue in Newton’s day, and he formulated his three laws in terms of a concept now called momentum, only later relating it to the concept of force. Nearly all modern texts start with force and do momentum later.

To many students, the statement in the example that the cable’s upward force “cancels” Earth’s downward gravitational force implies that there has been a contest, and the cable’s force has won, vanquishing Earth’s gravitational force and making it disappear. That is incorrect. Both forces continue to exist, but because they add up numerically to zero, the elevator has no center-of-mass acceleration. We know that both forces continue to exist because they both have side-effects other than their effects on the car’s center-of-mass motion. The force acting between the cable and the car continues to produce tension in the cable and keep the cable taut. Earth’s gravitational force continues to keep the passengers (whom we are considering as part of the elevator-object) stuck to the floor and to produce internal stresses in the walls of the car, which must hold up the floor.

The situation for a skydiver is exactly analogous. It’s just that the skydiver experiences perhaps a million times more gravitational force than the feather, and it is not until she is falling very fast that the force of air friction becomes as strong as the gravitational force. It takes her several seconds to reach terminal velocity, which is on the order of a hundred miles per hour.

More general combinations of forces

It is too constraining to restrict our attention to cases where all the forces lie along the line of the center of mass’s motion. For one thing, we cannot analyze any case of horizontal motion, since any object on Earth will be subject to a vertical gravitational force! For instance, when you are driving your car down a straight road, there are both horizontal forces and vertical forces. However, the vertical forces have no effect on the center of mass motion, because the road’s upward force simply counteracts Earth’s downward gravitational force and keeps the car from sinking into the ground.

The following slight generalization of Newton’s first law allows us to analyze a great many cases of interest:

Suppose that an object has two sets of forces acting on it, one set along the line of the object’s initial motion and another set perpendicular to the first set. If both sets of forces cancel, then the object’s center of mass continues in the same state of motion.

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