# Newton’s Laws

### Explaining the Motion

Science is the quest to understand nature in the most general terms possible. Newton’s laws of motion are among the most general, simple, and accurate laws possible, explaining innumerable phenomena—the motions of planets and billiard balls, falling objects and projectiles, human bodies and airplanes. They explain the motions of all things smaller than a star and larger than an atom, more or less. Technically, Newton’s laws are incorrect unless modified to be consistent with Einstein’s theory of relativity and quantum theory, but these corrections rarely make a difference at human scales of space, time, and energy—and even the laws of relativity and quantum theory stand on Newton’s shoulders. Let’s dig into the three laws of motion.

Godfrey Kneller. Portrait of Isaac Newton, 1689.

**Newton’s first law** states that all objects will continue moving at the same speed, in the same direction, unless acted on by external forces. This is the law of inertia. Standing still is a special case of this law, and in fact, stillness exists only relative to a frame of reference; everything in the universe is moving relative to some other things, so the law as first stated is sufficient. Galileo also figured out the first law, and Newton indeed gave him credit for it. Rene Descartes and Thomas Hobbes also entertained equivalent ideas, but they didn’t investigate them experimentally, as Newton did, nor express them as clearly.

You’re experiencing the first law of motion every time you are sitting in a moving car. According to the law, an object at rest will remain at rest unless acted upon by an external force. In this case, your body is at rest, and so it would remain in that state unless the car’s movement exerts a force on it. When the car suddenly accelerates, your body continues to remain in the same position until an external force (the backrest) pushes against it. Similarly, when the car comes to a sudden stop, your body continues to move forward due to its inertia until an external force, such as the seatbelt, stops it.

**Newton’s second law** states that the velocity of an object with constant mass will change in magnitude and direction in proportion to the force applied to it. Or, complementarily, that a change in velocity will generate such a force. This yields the best-remembered equation of high school physics (for us anyway!): F = ma, or force equals mass times acceleration.

Imagine pushing a shopping cart in a supermarket. The mass of the cart and the groceries it holds determine the amount of force required to push it. According to the law, the heavier the cart and the more groceries it holds, the more force is required to move it. Similarly, if you want to move the cart quickly, you will need to apply more force. If you apply too much force, the cart may move too quickly, and you may lose control of it. On the other hand, if you apply too little force, the cart may not move at all.

**The third law** is the one popularly known as “for every action, there is an equal and opposite reaction,” although Newton expressed it in terms of forces applied by one body to another. If the third law was not true, you would be able to put your finger through anything. Every time you push against something, it pushes back against you. Same for pulling—as anyone knows who’s ever towed something heavy by rope. If you jump, you push the Earth ever so slightly out of orbit. And when you come down, the gravitational attraction between you and Earth pulls it back into place (phew!).

Title page of Principia. First edition, 1687.

In 1687, Isaac Newton published the *Philosophiae Naturalis Principia Mathematica*, commonly known as *The Mathematical Principles of Natural Philosophy*. This groundbreaking book contained Newton’s three laws of motion, which, in combination with his theory of universal gravitation, explained Kepler’s laws of planetary motion. The impact of these laws has been immense, enabling humans to engineer numerous inventions such as flight, automobiles, rockets, and modern architecture.

Beyond their technological applications, Newton’s laws also had a profound impact on worldviews. They presented the universe as a mechanical, clockwork system, governed strictly by the equations of calculus, which Newton himself invented (in competition with Leibniz). This idea of nature as a machine continues to be a powerful metaphor, although the advent of quantum mechanics has shown that the universe is not strictly clockwork.

Nevertheless, Newton’s laws remain a quintessential example of the success of science. Their generality, precision, empirical basis, and infinite applicability make them a testament to the power of human reason and the scientific method. Even in the quantum realm, laws derived from Newton’s laws of motion play a fundamental role in describing the behavior of matter and energy.

### Quotes

“If I have seen further than others, it is by standing upon the shoulders of giants.” —Isaac Newton

“I can calculate the motion of heavenly bodies but not the madness of people.” ―Isaac Newton

“Tact is the knack of making a point without making an enemy.” —Isaac Newton

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