Laws of Motion

INTRODUCTION

The entire system of dynamics is based on three laws of motion, which are the fundamental laws, and were formulated by *Newton. Like other scientific laws, these are also stated in the mathematical forms which agree with actual observations.

IMPORTANT TERMS

The following terms, which will be mostly used in this chapter, should be clearly understood at this stage :

1. Mass. It is the matter contained in a body. The units of mass are kilogram, tonne etc.  Named after Sir Issac Newton, who enunciated theselaws in 1680.

2. Weight. It is the force, by which the body is attracted towards the centre of the earth. The units of weight are the same as those of force i.e. N, kN etc.

3. Momentum. It is the quantity of motion possessed by a body. It is expressed mathematically as Momentum = Mass × Velocity. The units of momentum depend upon the units of mass and velocity. In S.I. units, the mass is measured in kg, and velocity in m/s, therefore the unit of momentum will be kg-m/s.

4. Force. It is a very important factor in the field of dynamics also, and may be defined as any cause which produces or tends to produce, stops or tends to stop motion. The units of

force, like those of weight, are N, kN etc.

5. Inertia. It is an inherent property of a body, which offers resistance to the change of its state of rest or uniform motion.

RIGID BODY

Strictly speaking, the laws of motion, enunciated by Newton, are applicable only to the rigid  bodies. Though a rigid body (or sometimes written as ‘body’ for the sake of simplicity) is defined in

many ways by the different scientists, yet there is not much of difference between all the definitions. But the following definition of a rigid body is universally recognised. A rigid body consists of a system of innumerable particles. If the positions of its various particles remain fixed, relative to one another (or in other words, distance between any two of its particles remain constant), it is called a solid body. It will be interesting to know that in actual practice, all the solid bodies are not perfectly rigid bodies. However, they are regarded as such, since all the solid bodies behave more or less like rigid bodies.

NEWTON’S LAWS OF MOTION

Following are the three laws of motion, which were enunciated by Newton, who is regarded as father of the Science.

1. Newton’s First Law of Motion states, “Everybody continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force.”

2. Newton’s Second Law of Motion states, “The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts.”

3. Newton’s Third Law of Motion states, “To every action, there is always an equal and opposite reaction.”

NEWTON’S FIRST LAW OF MOTION

It states “Everybody continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force.” It is also called the law of inertia, and consists of the

following two parts :

1. A body at rest continues in the same state, unless acted upon by some external force. It appears to be self-evident, as a train at rest on a level track will not move unless pulled by

an engine. Similarly, a book lying on a table remains at rest, unless it is lifted or pushed.

2. A body moving with a uniform velocity continues its state of uniform motion in a straight line, unless it is compelled by some external force to change its state. It cannot be exemplified because it is, practically, impossible to get rid of the forces acting on a body.

Note. The second part of the law furnishes us with an idea about the function of a force. It also implies that a force, which is to produce a change in the rest or motion of a body must be externally impressed ; or in other words, must act from outside. A little consideration will show, that the effect of inertia is of the following two types :

1. A body at rest has a tendency to remain at rest. It is called inertia of rest.

2. A body in uniform motion in a straight line has a tendency to preserve its motion. It is called inertia of motion.

NEWTON’S SECOND LAW OF MOTION

It states, “The rate of change of momentum is directly proportional to the impressed force and takes place, in the same direction in which the force acts.” This law enables us to measure a force,

and establishes the fundamental equation of dynamics. Now consider a body moving in a straight line. Let its velocity be changed while moving.

Let m = Mass of a body,

u = Initial velocity of the body,

v = Final velocity of the body,

a = Constant acceleration,

t = Time, in seconds required to change the velocity from u to v, and

F = Force required to change velocity from u to v in t seconds.

∴ Initial momentum = mu

and final momentum = mv

ABSOLUTE AND GRAVITATIONAL UNITS OF FORCE

NEWTON’S THIRD LAW OF MOTION

It states “To every action, there is always an equal and opposite reaction.” By action is meant the force, which a body exerts on another, and the reaction means the equal and opposite force, which the second body exerts on the first. This law, therefore, states that a force always occurs in pair. Each pair consisting of two equal opposite forces. This law appears to be self-evident as when a bullet is fired from a gun, the bullet moves out with a great velocity, and the reaction of the bullet, in the opposite direction, gives an unpleasant shock to the man holding the gun. Similarly, when a swimmer tries to swim, he pushes the water backwards and the reaction of the water pushes the swimmer forward. Though the Newton’s Third Law of Motion has a number of applications, yet recoil of gun is important from the subject point of view.