Newton's Laws of Motion

Newton’s Laws of Motion

In order to put his system into mathematical form at all, Newton had to devise the concept of differential quotients and propound the laws of motion in the form of total differential equations—perhaps the greatest advance in thought that a single individual was ever privileged to make. —Albert Einstein

Newton’s laws describe classical motion in an inertial reference frame: a frame in which an object with no net external force moves at constant velocity.

These laws about the relationship between force, speed and motion of bodies are the basis of classical mechanics and physics, and were postulated by the English physicist and mathematician Isaac Newton, in 1687.

Building on ideas from Galileo and Descartes, Newton set out the laws in his 1687 book Philosophiæ naturalis principia mathematica. Together with his law of gravitation, they connected the motion of objects on Earth with the motion of celestial bodies.

And thus, nature will be very conformable to herself and very simple, performing all the great motions of the heavenly bodies by the attraction of gravity which intercedes those bodies, and almost all the small ones of their particles by some other attractive and repelling powers which intercede the particles. The vis inertiae is a passive principle by which bodies persist in their motion or rest, receive motion in proportion to the force impressing it, and resist as much as they are resisted. By this principle alone there never could have been any motion in the world. Some other principle was necessary for putting bodies into motion; and now they are in motion, some other principle is necessary for conserving the motion. —Newton

INERTIA - NEWTON’S FIRST LAW

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. —Newton

Inertia is resistance to a change in velocity. An object does not require a continuing net force to keep moving at constant velocity.

Inertia is the first law of history, as it is of physics. — Morris Raphael Cohen

An object remains at rest or moves in a straight line at constant speed when the net external force is zero. Individual forces may still act on it, provided they balance.

Nothing happens until something moves. — Albert Einstein

Greater mass means greater inertia: producing the same acceleration requires more net force.

FORCE - NEWTON’S SECOND LAW

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. — Newton

For a body of constant mass in an inertial frame, the net external force equals mass times acceleration:

F = ma

Force and acceleration have directions. A force can change speed, direction, or both. With the same mass, a larger net force produces greater acceleration; with the same net force, a larger mass produces less acceleration.

More generally, the net external force equals the rate of change of momentum of a fixed collection of matter. When analyzing a system whose mass changes, such as a rocket losing fuel, the momentum carried into or out of the system must also be accounted for.

ACTION / REACTION - NEWTON’S THIRD LAW

For every action, there is an equal and opposite reaction. —Newton

If object A exerts a force on object B, object B exerts an equal and opposite force on object A. These forces act on different objects, so they do not cancel in the force balance for either object alone.

When you push a car, the car pushes back on you even though it has no intention of doing so. Whether you move depends on the other forces acting on you, including friction with the ground. An equal reaction force does not by itself mean you must move backward.

Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. He looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher’s treasure hunt to the esoteric brotherhood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements […], but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia. —John Maynard Keynes