# Galilean transformation of non-inertial frame

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• lriuui0x0
In summary: As pointed out, it’s not actually clear what you mean by a Galilean transformation between two non-inertial frames.
In the restframe of the Earth, i.e., our usually used frame for experiments, we have an approximately inertial frame and we can take the gravitational force of the Earth into account in the approximation of ##\vec{F}_G=m \vec{g}## with ##\vec{g}=\text{const}##. Equivalently you can switch to a freely falling frame within this approximation of a constant gravitational force. Then you are really in an inertial frame.

This is, however of course, an approximation, and the Earth-fixed frame is not an inertial frame, because of the rotation of the Earth around its axis, leading to nice phenomena like Foucault's pendulum.

Today the best realization of a real inertial frame is to use a freely-falling reference frame, where the cosmic-microwave background radiation is at rest, i.e., is really homogeneous and isotropic (neglecting the otherwise very important fluctuations of its temperature at the order of ##10^{-5}##), but that's another story.

valenumr
<h2>1. What is the Galilean transformation of non-inertial frame?</h2><p>The Galilean transformation of non-inertial frame is a mathematical concept used in classical mechanics to describe the relationship between two reference frames that are accelerating relative to each other. It allows for the transformation of physical quantities, such as position and velocity, between these frames.</p><h2>2. How does the Galilean transformation differ from the Lorentz transformation?</h2><p>The Galilean transformation is only valid for objects moving at speeds much slower than the speed of light, whereas the Lorentz transformation accounts for the effects of special relativity, including time dilation and length contraction, at high speeds.</p><h2>3. What is an inertial frame of reference?</h2><p>An inertial frame of reference is a reference frame in which Newton's laws of motion hold true. This means that an object in motion will continue to move at a constant velocity unless acted upon by an external force.</p><h2>4. How does the Galilean transformation account for non-inertial forces?</h2><p>The Galilean transformation does not account for non-inertial forces, such as centripetal force, that may be present in a non-inertial frame. These forces must be included separately in the equations of motion.</p><h2>5. Can the Galilean transformation be used in all situations?</h2><p>No, the Galilean transformation is only applicable in situations where the relative velocities between frames are much smaller than the speed of light. In cases where high speeds are involved, the Lorentz transformation must be used instead.</p>

## 1. What is the Galilean transformation of non-inertial frame?

The Galilean transformation of non-inertial frame is a mathematical concept used in classical mechanics to describe the relationship between two reference frames that are accelerating relative to each other. It allows for the transformation of physical quantities, such as position and velocity, between these frames.

## 2. How does the Galilean transformation differ from the Lorentz transformation?

The Galilean transformation is only valid for objects moving at speeds much slower than the speed of light, whereas the Lorentz transformation accounts for the effects of special relativity, including time dilation and length contraction, at high speeds.

## 3. What is an inertial frame of reference?

An inertial frame of reference is a reference frame in which Newton's laws of motion hold true. This means that an object in motion will continue to move at a constant velocity unless acted upon by an external force.

## 4. How does the Galilean transformation account for non-inertial forces?

The Galilean transformation does not account for non-inertial forces, such as centripetal force, that may be present in a non-inertial frame. These forces must be included separately in the equations of motion.

## 5. Can the Galilean transformation be used in all situations?

No, the Galilean transformation is only applicable in situations where the relative velocities between frames are much smaller than the speed of light. In cases where high speeds are involved, the Lorentz transformation must be used instead.

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