Frame of Reference – Inertial and Non Inertial Frame of Reference

FRAME OF REFERENCE – INERTIAL AND NON-INERTIAL FRAME OF REFERENCE

FRAME OF REFERENCE

A frame of reference is a coordinate system relative to which the position and motion of a body may be described.

“So, a frame of reference is a part of the description of the motion.”

The simplest frame of reference is the Cartesian system of coordinates, in which the position of the particle or body is specified by its three coordinates x, y, z along the three perpendicular axis.

If at any instant, the position vector drawn from the origin to the particle is given by 

The position vector should be expressed as function of time, then the velocity and acceleration of the particle can be determined as 

So in general for the location of an event in frame of reference we require its position and time of occurrence for a coordinate (x, y, z, t).

TYPES OF FRAME OF REFERENCE

Frame of Reference is of two types:

1.      INERTIAL FRAME OF REFERENCE

When bodies in a frame of reference obey Newton’s Law of Inertia and Other Law of Newtonian Mechanics, This Frame is called Inertial Frame of Reference. In this case, No external force acts on the body. It is either at rest or moving with constant velocity.

Thus in an inertial frame, if a body does not experience any external force, its acceleration a is given by

IS EARTH AN INERTIAL FRAME?

The earth is not really an inertial frame of reference because of its orbital motion about the sun and rotational motion about its own axis. In both these motion, Centripetal acceleration are present, so any frame of reference set up earth or earth itself, as is where is cannot be considered as an inertial frame of reference but in the present study we are considering speed of the order of 3 lakh km per second and earth is moving only with 30 km/s, so the effect of and revolution of earth may be ignored. Thus for all practical purposes, earth or any frame of reference set up on earth is regarded as an Inertial Frame of Reference.

2.      NON-INERTIAL FRAME OF REFERENCE

When a body is accelerated in a frame of reference, the frame of reference is called Non-Inertial Frame of Reference. The law of Inertia is not valid for an accelerated Frame of Reference.

The simplest example of a Non-Inertial Frame is provided by a rotating merry-go-round.

Theory of Relativity, Relativistic Mechanism, Einstein Theory of Relativity

THEORY OF RELATIVITY, EINSTEIN THEORY OF RELATIVITY

The theory that deals with relativity motions of bodies is called Theory of Relativity. The Theory of Relativity shows that the Classical Mechanics is not applicable to bodies moving with velocity nearer to the velocity of light. According to Classical Theory, Space and Time are absolute. The flow of time is assumed to be confirmed in all situations, the movement of time and time intervals are identical in all frames of reference and that, similarly, lengths are also identical in all frames. But these concepts are not valid at high velocities. The theory of Relativity provides many new concepts such as:

1)      The length of a moving body contracts in the direction of motion.

2)      Clock in motion slow-down.

3)      At high speed, speed and time are no more separate but merge into space-time continuous.

4)      The mass of a moving body is greater than its mass when at rest.

CONCEPT OF RELATIVITY

(A)   Let us consider a river flowing and two persons (A and B) are standing on the banks of the river facing towards each other. Now the person A will say that house is on the right side while the Person B will say that house is on the left side. But actually the position of house is fixed. This indicates that position is relative.

(B)   If someone asks whether ball is large or small? If we compare the ball with earth then we will say that ball is small but if we compare the ball with an atom, then we will say that ball is large. This indicates that size is relative.

Similarly time and motion are also relative.