Non-Inertial Frame of Reference

  • A frame that undergoes acceleration relative to an assumed inertial frame is termed non-inertial, where Newton’s laws do not hold true.
  • To apply Newton’s laws in a non-inertial frame, we introduce a fictitious force known as a pseudo force.
  • Non-inertial frames are characterized by varying velocities or accelerations, unlike inertial frames which move at constant speeds.
  • Examples of non-inertial frames include vehicles traveling along a circular road or accelerating in a straight line, where objects experience acceleration.
  • Compared to the default inertial coordinate system, non-inertial coordinate systems are accelerated, often indicated by non-zero accelerometer readings.
  • For instance, when a car accelerates from a standstill at a traffic light, it enters a non-inertial frame until reaching a constant velocity, during which accelerometers detect acceleration.

Lorentz Transformations

Lorentz factor, often known as the Lorentz term, is a measurement that describes an object’s measurements of time, length, and other physical properties, which vary when it moves. The expression occurs in derivations of the Lorentz transformations and is found in a number of special relativity equations.

It is named after the Dutch physicist Hendrik Lorentz, the term originates from its earlier use in Lorentzian electrodynamics. 

Table of Content

  • Lorentz Factor Definition
  • Inertial Frame of Reference
  • Non-Inertial Frame of Reference 
  • Difference between Inertial Frame of Reference and Non-Inertial Fames of Reference
  • Lorentz Transformation
  • The formula for Lorentz transformation can be given as,
  • Time Dilation
  • Properties of Lorentz Factor
  • Solved Examples on Lorentz Factor

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Lorentz Factor Definition

Lorentz factor is the factor that describes the dilated time of a moving clock evaluated in a stationary frame in the time dilation formula....

Inertial Frame of Reference

An inertial frame of reference is defined as a frame that is either stationary or moves at a constant speed relative to an imaginary inertial reference frame. Within an inertial frame, a hypothetical inertial coordinate system is established, surrounded by an environment that adheres to Newton’s laws of motion. Newton’s laws hold true in inertial frames, meaning objects within these frames will remain at rest or continue moving uniformly unless acted upon by an external force. A reference frame serves as an environment to measure the motion of objects, and if Newton’s laws are valid, any uniformly rotating reference system must also follow the law of inertia. Examples of inertial reference systems include platforms at rest, such as a train station platform, where objects satisfy the law of inertia due to the absence of acceleration within the frame....

Non-Inertial Frame of Reference

A frame that undergoes acceleration relative to an assumed inertial frame is termed non-inertial, where Newton’s laws do not hold true. To apply Newton’s laws in a non-inertial frame, we introduce a fictitious force known as a pseudo force. Non-inertial frames are characterized by varying velocities or accelerations, unlike inertial frames which move at constant speeds. Examples of non-inertial frames include vehicles traveling along a circular road or accelerating in a straight line, where objects experience acceleration. Compared to the default inertial coordinate system, non-inertial coordinate systems are accelerated, often indicated by non-zero accelerometer readings. For instance, when a car accelerates from a standstill at a traffic light, it enters a non-inertial frame until reaching a constant velocity, during which accelerometers detect acceleration....

Difference between Inertial Frame of Reference and Non-Inertial Fames of Reference

Aspect Inertial Frame of Reference Non-Inertial Frame of Reference Definition Moves at constant speed or is stationary Undergoes acceleration relative to an inertial frame. Validity of Newton’s Laws Newton’s laws of motion hold true Newton’s laws of motion do not hold true Pseudo Force Requirement No requirement for pseudo forces Pseudo forces are needed to apply Newton’s laws Motion Characteristics Uniform motion or at rest Varying velocities or accelerations Accelerometer Readings Typically zero accelerations Non-zero accelerations may be detected Examples Stationary platform, constant velocity motion Circular motion, accelerating vehicle...

Lorentz Transformation

The Lorentz transformations are a one-parameter family of linear transformations from a frame in spacetime that is in a fixed position to a frame that is moving with constant speed. These transformations are named after a Dutch physicist, Hendrik Lorentz....

The formula for Lorentz transformation can be given as,

t’ = γ(t – (vx)/c2) x’ = γ(x – vt) y’ = y  z’ = z where, (t, x, y, z) and (t’, x’, y’, z’) are the coordinates of event in two frames.v is restricted velocity to x-direction.c is speed of light...

Time Dilation

Either a difference in gravitational potential between their locations or the relative velocities between the two frames of reference produce time dilation (gravitational time dilation taken from general relativity). “Time dilation” describes the velocity-related effect, when it cannot be determined....

Properties of Lorentz Factor

Following are the properties of Lorentz Factor...

Solved Examples on Lorentz Factor

Problem 1: If the relative velocity between the two observers is 120 m/s, Determine the Lorentz factor. (Speed of light is 3 x 108 m/s)....

Lorentz Transformations-FAQs

What is the Lorentz force?...