The frame of reference

Introduction

The frame of reference can be defined as an arbitrary set of axes used to describe the position or motion of something or to develop physical laws. One of the most fundamental notions in kinematics is the frame of reference.

Definition

In dynamics, a reference frame, also known as a frame of reference, is a set of graded lines symbolically tied to a body that characterizes the position of points relative to the body.

Coordinate systems are reference frames used in dynamics, having axes (lines) originating from a point known as the origin. Two integers can be used to indicate the position of a point traveling parallel to a plane (plane motion):

(1) the distances between a point and two lines on the plane that are at right angles to one another (rectangular coordinates)

(2) the length of a line with one end fixed at the origin and the other end at the moving point, as well as the angle the line makes with a fixed axis (polar coordinates).

An abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements inside that frame make up a frame of reference.

Types

Once we’ve decided on a frame of reference, we can have two types of reference frame:

•     Inertial Reference Frame
•     Non-inertial reference frame

Inertial frame of reference

A frame of reference in which Newton’s law holds good is called an inertial frame of reference. That is to say, if no external force acts on a body, it will remain at rest or in uniform motion.

The word inertial frame refers to a reference frame that is assumed to be the inertial frame of reference. An inertial frame is at rest or moves with constant velocity concerning an imagined inertial reference frame.

Galilean transformations are used to convert several physical parameters from one inertial frame of reference to another, including location coordinates, velocity, acceleration, time, and so on.

Galilean transformation equations are:

 x’=x-vt, y’=y, z’=z, t’=t.

Examples:

•     Our planet.
•     With the earth, a space shuttle moves at a constant speed.
•     With the earth, a rocket moves at a constant velocity.

The non-inertial frame of reference

A non-inertial frame is accelerated relative to the supposed inertial frame of reference. In these frames, Newton’s law will not apply.

Newton’s second law, ‘F = ma,’ cannot be applied to an object without taking into account the additional force acting on it due to the accelerated frame. In certain publications, fictitious force is referred to as pseudo force.

Like a gravitational force, the fictitious force experienced in a uniformly accelerating system is uniform and proportional to the mass of the system. The imaginary forces are caused by the coordinate system’s acceleration rather than by interactions between bodies.

Examples:

•     The frame could be traveling in a straight path but increasing or decreasing its speed.
•     The frame could be moving at a constant pace along a curved course.
•     The frame could be speeding up or slowing down as it travels along a curving path.

To fully define a reference frame in n dimensions, n + 1 reference points are sufficient. A reference frame with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes can be defined using rectangular coordinates.

The Special Theory of Relativity by Albert Einstein

The “Special Theory of Relativity” is the section of relativistic physics that deals with uniform motion.

The following fundamental postulates underpin Einstein’s special theory of relativity:

1. Relativity Principle – In all inertial frames of reference, the rules of physics are the same.
2. Constant speed of light principle – The speed of light in free space is constant.

Einstein’s theory resulted in the introduction of new coordinate transformations between inertial frames of reference, known as Lorentz transformations. These transformations were nearly identical to the classical model at slow speeds, but at high speeds, they were nearly identical to the classical model. They produced significantly different results at the speed of light.

Conclusion

A frame of reference is a coordinate system with a time frame. Objects in motion are those that change position over time for the frame of reference, whereas those that do not move position are said to be at rest.