Before studying Newton’s laws of motion, we shall understand a very important concept of reference frames in this article.

Motion is a Relative Concept:

Motion is always with respect to the observer. Consider a person A is standing in a train moving in the north direction with a uniform velocity of 5 m/s in a straight line. Let us consider another person B standing on the ground.

Now B as an observer would say that he himself is stationary and the person A is moving in the north direction with a uniform velocity of 5 m/s. Now A as an observer would say that he himself is stationary and the person B is moving in the south direction with a uniform velocity of 5 m/s.

Thus there is a difference in the interpretation of motion of each other it is because their states of motion are different. It is to be noted that both are in the state of uniform motion with respect to earth. Thus we can say that the motion is a relative concept and not the absolute one.

Reference Frame:

It is a system of co-ordinate axes with reference to which position or motion of an object in space is described. The rectangular Cartesian coordinate system of axes is considered as the simplest reference system.

If (x, y, z) are the coordinates of the point in this system of reference, then the position vector of the particle w.r.t. the origin is given by

Let us consider two persons A and B traveling by train with uniform velocity 5 m/s towards right as shown.

There is a third observer C standing on the ground near the track. observer A and B are moving with uniform velocity w.r.t. earth similarly observer C is at rest w.r.t. earth. Hence A, B, C are the inertial frame of reference. We shall ask an opinion of motion of each observer. A will say that he is stationary, B is stationary and C is moving backward with uniform velocity 5 m/s and no force is acting on him. The opinion of B will be similar. But C will say he is stationary and B and C are moving towards the right with uniform velocity 5 m/s. No force acts on them. Then who is correct. Everybody is correct because the motion is always with respect to the state of the observer. Thus Newton’s laws are not violated.

Concept of Inertial Reference Frame:

The reference frame which is at rest or moving with uniform velocity with respect to earth is called inertial reference frame.

Characteristics of Inertial Reference System:

• The reference frames which are at rest or moving with uniform motion with respect to earth are called as inertial reference frames.
• Newton’s laws of motion are applicable in inertial reference frames
• Concept of pseudo force is not required in inertial reference frames.
• A person sitting in a car moving with uniform motion in a straight line is the inertial frame of reference.

Concept of Non-Inertial Reference Frame:

The reference frame which is moving with uniform acceleration w.r.t. earth is called non-inertial reference frame

Characteristics of Non-inertial Reference System:

• The reference frames which are moving with acceleration with respect to earth are called non-inertial reference frames.
• Newton’s laws of motion are not applicable in non-inertial reference frames.
• To apply Newton’s laws of motion in non-inertial reference frames we have to consider the existence of an imaginary force called pseudo force.
• A person sitting in a car negotiating a curve is non-inertial frame of reference.

Distinguish between inertial reference frame and non inertial reference frame.

Concept of Pseudo Force:

Pseudo force is imaginary or hypothetical force whose existence is to be granted in non inertial reference frames so that Newton’s laws of motion are applicable in non inertial reference frame.

Let us consider two persons A and B traveling by train with uniform acceleration 5 ms^-2 towards the right as shown. There is a third observer C standing on the ground near the track. observer A and B are moving with uniform acceleration w.r.t. earth while observer C is at rest w.r.t. earth. Hence A and B are the non-inertial frame of reference, while C is still inertial frame of reference.

We shall ask the opinion of motion of each observer. C will say he is stationary and B and C are moving towards the right with uniform acceleration 5 m/s². Necessary force for acceleration is provided by the engine of the train. Thus he is not violating Newton’s laws of motion. 

A or B will say that he is stationary and C is moving backward with uniform acceleration 5 m/s² and no force is acting on C. It is a contradiction to Newton’s laws of motion because he is saying acceleration is there but no force present to cause it. Thus Newton’s laws of motion are violated in the non inertial reference frame.

To correct A and B the observer in non-inertial reference frame, imaginary or hypothetical force acts on C. This force is called pseudo force.

Examples of Pseudo Forces:

An object revolving in a circle experiences a centrifugal force directed radially outward. This force tends to move the object away from the centre. This centrifugal force is a pseudo force because the circular motion accelerated motion. Thus the object is in acceleration w.r.t. earth. The reference frames which are moving with acceleration with respect to earth are called non-inertial reference frames.

When bus negotiates a curve on the right side, the passengers are pushed on the left side and if the bus negotiates a curve on left side passengers are pushed on the right side. As the bus is negotiating a curve the passengers are in accelerated motion. Thus they constitute the non-inertial reference frame.

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