Newton\'s Three Laws of Motion

Newton's Three Laws Of Motion

Three laws of motion, published in 1687 by Sir Isaac Newton in his work Philosophiae Naturalis Principia Mathematica, formed the basis of modern classical mechanics and dynamics. These laws were initially explained on the example of simple physical objects, but their application expands over objects of different nature and in general, classical physics of universe is based on them. Newton's three laws of motion supplemented knowledge of physics and mechanics and gave a deeper explanation of law of universal gravitation and Kepler's laws of planetary motion. Systematization of dynamics and motion knowledge, which is provided by these laws on the hand with mathematical apparatus of calculus, gave an impulse to the development of different branches of physics: mechanics and its brunches, electromagnetism, optics, molecular physics.

Three Newton laws are postulated as follows:

First Law: Objects in motion tend to stay in motion, and objects at rest tend to stay at rest unless an outside force acts upon them.

Second law: The rate of change of the momentum of a body is directly proportional to the net force acting on it, and the direction of the change in momentum takes place in the direction of the net force.

Third law: To every action (force applied) there is an equal but opposite reaction (equal force applied in the opposite direction).

The first law is also called law of inertia or principle of Galileo, saying that uniform motion is motion with constant velocity (constant speed in linear path). Constant velocity also implies that the object moves without acceleration and that the net force (or vector sum of forces which act on the object) equals to zero. The first law of motion states that a resting object will move only when forces acts upon it and moving object will not experience change in velocity until it experiences force upon it. The first law seems to be very easy for understanding and quite obvious, but at the same time it's impossible to prove it directly under usual conditions. There are not objects, which will be moving with constant velocity forever, and there are no objects, which are at rest forever: friction forces, microscopic dynamics and other factors contribute to interruption of inertia. It's a well-known fact that a launched ball or hockey puck will not be in motion forever as gravitational force, friction force and air resistance slow motion, which always stops.

The second law, which states that rate of change of object's momentum is proportional to the force exerted upon it is the most practical law. This law is the logical continuation of the inertia law and explanation of Galileo's principle and transformations. Second law gives a prediction to what will happen with the object when a force acts on it: object's velocity will change and object will accelerate (with negative or positive acceleration). In order to understand the meaning of this law, mass is introduced. The mass of the object is a quantitative measure of inertia, which defines amount of matter contained in object. That's why in modern interpretation the second law says that objects acceleration is directly proportional to the magnitude of the total force and inversely proportional to the mass of the object. That's why mass of the object also defines object's resistance to acceleration.

In terms of mathematics, second law can be written as a differential equation:

where F. is force, k is proportionality coefficient, v is objects velocity and m is object's mass.

If a is acceleration is a constant, second law can be simplified to:

or in SI units.

Third law states that forces, which occur in pairs, are equal in magnitude, but are oppositely directed. Third law is mathematical conclusion of the law of conservation of momentum (as it can be stated that acceleration is a derivative of velocity and force is a derivative of momentum). Third law states that though forces of interaction are equal, accelerations may be different as masses of objects may be not the same.