CHAPTER 3 : DYNAMICS

3.1 Dynamics of a particle

Introduction

The laws of motion formulated by Newton are the pillars that establish the cause (Force) and the effect (Acceleration) relation. These causal relations provide for the analysis and prediction of motion. Newton formulated the laws of motion based on Galileo's experiments dealing with rolling bodies within inclined planes. These laws are abstractions or idealizations of the experimental observations.

Newton's Laws of Motion

First Law

An object at rest or in uniform motion in a straight line continues to maintain the state of rest or uniform motion unless an unbalanced external force is applied to it. This law essentially defines force as the cause of change in a state of rest or of uniform motion in a straight line i.e. acceleration. It also defines a property of matter called Inertia as that property, which does not let the object acquire acceleration by itself.

Note : Uniform motion in a straight line means constant velocity.

That part of the statement of the first law about objects at rest is a factual statement. But the part concerning uniform motion in a straight line is an idealization of actual observations; the idealization demands that roads are perfectly smooth, leveled in horizontal plane and literally infinite in extent. Surely such a state of affairs can never be realized. The important point to be noted is that force is the cause of acceleration, whether the acceleration is due to a change in the state of uniform motion or is due to change in state of rest. It must have occurred to you that the state of rest and the state of uniform motion are equivalent; the difference lies in the frame of reference chosen for determining the state of motion.

The measure of the inertia of an object is the mass of the object. What is the mass of an object ? It is dangerous to try and define what is mass, therefore we shall not define it, but agree that all of us initially understand what it means. Of course, we will explain the method to measure it, but for that we shall have to wait till the second law.

The other name for the First law is the Law of Inertia, as it defines the property of Inertia.

Second Law

It is understood that it is an unbalanced, external force.

[The choice of unit of force is 1n - 1 Newton -when m = 1 kg and a = 1 m/s²]

Index

3.1 Dynamics of a particle
3.2 Dynamics of a system of particles
3.3 Law of Conservation of Momentum

Chapter 4