Newton's laws of motion

The laws of motion (laws of inertia) are the three scientific laws which Isaac Newton described; regarding the motion of bodies. These laws are fundamental to classical mechanics.

Newton first defined these laws in Philosophiae Naturalis Principia Mathematica (1687) and, using his newly developed calculus, proved many results concerning "idealised" particles. 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. Newton's laws were modified, in 1916, by Einstein's theory of relativity.

Table of contents

1 Newton's First Law (Law of Inertia) 2 Newton's Second Law 3 Newton's Third Law

Newton's First Law (Law of Inertia)

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 (forever and in the same manner), 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.

This is expressed by the equation:

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

This equation expresses that the more force an object receives, the greater its acceleration will be. The quantity m, or mass, in the above equation is the constant of proportionality, and is a characteristic of the object. This equation, therefore, indirectly defines the concept of mass.

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.

If you strike an object with a force of 200 N, then the object also strikes you (with a force of 200 N). Not only does a bullet exert force upon a target; but, the target exerts equal force upon the bullet. Not only do planets accelerate toward stars; but, stars accelerate toward planets. The reaction force has the same line of action, and is of the same type and magnitude as the original force.