CLASSICAL MECHANICS
Specificity of Newton's laws for objects with variable mass

Newton's laws of motion

Newton's laws of motion (also called the laws of inertia) are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. These laws are fundamental to classical mechanics.

Newton first published these laws in Philosophiae Naturalis Principia Mathematica (1687) and used them to prove many results concerning the motion of physical objects. In the third volume (of the text), he showed how, combined with his Law of Universal Gravitation, the laws of motion would explain Kepler's laws of planetary motion.

Importance of Newton's laws of motion

Nature and Nature's laws

lay hid in night;

God said, "Let Newton be!"

And there was light.

-- Alexander Pope

Newton's laws of motion, together with his Law of Universal Gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena such as: the motion of spinning bodies, motion of bodies in fluids; projectiles; motion on an inclined plane; motion of a pendulum; the tides; the orbits of the Moon and the planets. The law of conservation of momentum, which Newton derived as a corollary of his second and third laws, was the first conservation law to be discovered.

Newton's laws were verified by experiment and observation for over 200 years, until 1916, when they were superseded by Einstein's theory of relativity. Newton's laws still provide a completely adequate approximation for the behaviour of objects in "everyday" situations.

Newton's First Law

Alternative formulations:

• Every object persists in its state of rest, or uniform motion (in a straight line; unless, it is compelled to change that state, by forces impressed on it.
• A body remains at rest, or moves in a straight line (at a constant velocity), unless acted upon by a net outside force.

This means that a stationary object will remain stationary, and a moving object will continue to move (in a straight line and at a constant speed), unless a force acts upon it. In everyday life, the force of friction usually acts upon moving objects. Newton's law indicates that some force (gravity) must be acting upon the planets, as they do not travel in a straight line.

Newton's Second Law

Alternative formulations:

• The time rate of change in momentum is proportional to the applied force and takes place in the direction of the force.
• The acceleration of an object is proportional to the force acting upon it.

• F = ma
  • F = force
  • m = mass
  • a = acceleration.

In the equation, F = ma, a is directly measurable but F is not. The second law only has meaning if we are able to assert, in advance, the value of F. Rules for calculating force include Newton's Law of Universal Gravitation.

Taken together with Newton's Third Law of Motion, it implies the Law of Conservation of Momentum.

Newton's Third Law

Alternative formulations:

• Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body.
• For every action, there is an equal and opposite reaction.