# Definition of inertial reference frames

• throneoo
In summary, an inertial frame is a frame of reference in which Newton's first law applies - meaning that objects subject to zero net external force will move at a constant velocity. However, this definition can be circular as Newton's first law itself is only valid under inertial frames. Some texts define it without direct reference to Newton's first law, but this may not fully address the issue. There are also discrepancies in determining the exact inertialness of a frame, so we use the frame in which Newton's laws work well and declare it as inertial enough.
throneoo
What is the definition of an inertial frame ? I've read that Inertial frames are reference frames in which Newton's first law applies (i.e.bodies subject to zero net external force moves at constant velocity) , however Newton's 1st law itself is only valid under inertial frames. I find it weird because that would make inertial frames circularly-defined.
some texts define it without direct reference to "Newton's 1st law", defining as "frames in which an object subject to no net external force moves in constant velocity" , but I don't think that addresses the issue at all. Are there any alternative definitions?

It doesn't make it circularly defined. Newton came up with this idea: an object's velocity will not change unless there is some net force on the object. We define non inertial frames as frames where this idea doesn't apply. We have a law, and we have a name for situations in which the law doesn't apply.

Alternately, you could simply say a noninertial frame is a frame of reference that undergoes no acceleration.

throneoo said:
I find it weird because that would make inertial frames circularly-defined.
All of physics is based on connected definitions like this. For example: Charge is what is affected by electric field. The electric field is what affects charges. It's not circular, but merely defining two terms at the same time, based on their relation.

throneoo
axmls said:
Alternately, you could simply say a noninertial frame is a frame of reference that undergoes no acceleration.

Should this be an 'inertial' frame and not a 'noninertial' frame?

Yes it should. My mistake.

throneoo said:
What is the definition of an inertial frame ? I've read that Inertial frames are reference frames in which Newton's first law applies (i.e.bodies subject to zero net external force moves at constant velocity) , however Newton's 1st law itself is only valid under inertial frames. I find it weird because that would make inertial frames circularly-defined.
some texts define it without direct reference to "Newton's 1st law", defining as "frames in which an object subject to no net external force moves in constant velocity" , but I don't think that addresses the issue at all. Are there any alternative definitions?

Yes, that's the non-relativistic definition. The feeling of weirdness is understandable but mechanics is not wrong because of this. It is just that Newton's laws can be applied with lot of success in some frames and with little success in others.

For example, motion of the Moon around the Earth can be well analyzed with Newton's laws and with assumption that Earth is an origin of an inertial frame (axes pointing to distant stars). However, the motion of the Sun around the Earth cannot be successfully analyzed this way. Instead, one may describe motion of the Earth from the frame centered in the Sun (with axes pointing to distant stars) and then translate the results to the frame of the Earth.

Originally, Newton formulated his laws with respect to absolute space - there was no concept of inertial frame. However, absolute space has not been detected, has been frowned upon and Newton's laws were reformulated with inertial frames instead. This has made the system logically OK but how to ascertain whether system is inertial is not easy. There is no way to ascertain exact inertialness of a frame - there may and usually always are discrepancies. Often these are negligible, so we simplify and say Earth is inertial system, or solar frame is inertial system based on the question at hand. We use Newton's laws in the frame they apparently do work well and pronounce that frame as inertial enough.

throneoo

## What is an inertial reference frame?

An inertial reference frame is a coordinate system in which the laws of physics hold true without any external forces acting on it. In other words, an object in an inertial reference frame will either stay at rest or continue moving in a straight line at a constant speed, unless acted upon by an external force.

## Why is it important to define inertial reference frames?

Inertial reference frames are important because they provide a consistent and reliable way to measure and observe the behavior of objects in motion. They allow scientists to accurately describe and predict the motion of objects in the universe.

## How are inertial reference frames different from non-inertial reference frames?

An inertial reference frame remains at rest or moves at a constant velocity, while a non-inertial reference frame experiences acceleration or deceleration. This means that the laws of physics may not hold true in a non-inertial reference frame.

## Can there be multiple inertial reference frames in the same system?

Yes, there can be multiple inertial reference frames in the same system. For example, a person standing on a train may be in an inertial reference frame, while someone outside the train observing its motion may also be in an inertial reference frame.

## How do we determine if a reference frame is inertial or non-inertial?

A reference frame is considered inertial if an object's motion only depends on its initial velocity and any external forces acting on it. If an object's motion appears to be affected by fictitious forces, such as centrifugal force, then the reference frame is non-inertial.

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