Newton's Laws of Motion

I. Introduction

Kinematics is the study of motion, without reference to their causes. Dynamics is the study of motion along with their causes.

Are all motions explained by Newton's Second Law? No

* Ordinary, daily life motions of macroscopic objects are governed by Newton's Laws of Motion--particularly his second law.

Examples: movement of the body, a traveling car, a flying airplane

* For objects moving at speeds not very far (10^-5 or 10^-6 x C) below the speed of light in vacuum, motions are governed by Einstein's Theory of Relativity.

* For the motions of microscopic particles (electrons, protons, etc.) while they are in atoms, molecules, or solids, Newton's Laws do not apply. Quantum Mechanics explains these motions.

II. Newton's Second Law of Motion

An object of mass m moving at a velocity v possesses a linear momentum

The total linear momentum, , of a system of particles is the sum of the momenta of the individual particles.

Newton's Second Law:

The time rate of change, , of the linear momentum of an object is equal to the sum of the external forces acting on that object. For a system of particles:

M is the total mass and is the velocity of the center of mass of the system of particles. For a system of particles, Newton's second law is

Note:

. For a system with M=constant, .

So, for m = constant or for M=constant, we have

The Law of Conservation of Linear Momentum

When the net force is equal to zero, the total linear momentum is constant.

III. Newton's First Law

If

Note: If , for a fixed mass m, the velocity is constant. Hence, (a) the motion is linear and uniform (if the constant is not zero) and remains that way until the object is acted on by an external force OR (b) the object is at rest (if the contant is zero) and remains that way until acted upon by an external force.

IV. Newton's Third Law

For mechanical systems, action and reaction forces are equal in strength and opposite in orientation.

Secret: Action and reaction are applied to different objects. The action by the book is applied to the table and the reaction of the table is applied to the book.

Note:

APPLICATIONS: master operations on vectors to apply Newton's laws.

We have already seen above how Newton's second law leads directly to (a) the law of conservation of the total linear momentum of a system or of the linear momentum of a single particle and to (b) Newton's first law.

It is critical to note that in applying Newton's second law, the major source of error is the failure of the problem solver to identify and add all the external forces to get the net external force that is equal to the time rate of change of the total linear momentum (or to mass times acceleration, if M is constant).

Finally, we should learn that "for all collisions of particles, the net external force on the colliding particles is assumed to be zero! "