# B How to check if frame is inertial?

Tags:
1. Mar 9, 2016

### hackhard

inertial frame is one in which isolated particle has constant velocity
but is there actually any "isolated particle " ?
how then can frame be defined as or not being inertial ?
or is it that -
for a system in which acceleration due to external forces is equal for all members ,
the frame of member whose acceleration due to internal forces is negligible
(compared to acceleration due to internal forces of other members) is considered inertial for analyzing motion of other members of system

2. Mar 9, 2016

### Staff: Mentor

Attach an accelerometer to the particle. If the accelerometer reads 0 then the particle is "isolated" in the necessary sense.

3. Mar 9, 2016

### FactChecker

The real problem with using an accelerometer would be in distinguishing between acceleration and gravity.

4. Mar 9, 2016

### bcrowell

Staff Emeritus
There are two different definitions of an inertial frame, one in Newtonian physics and one in relativity.

Of the four forces of nature, three can be shielded against, so a particle can be isolated from them in a well-defined sense. However, we don't have gravitational shielding, and the equivalence principle guarantees that gravitational shielding can't exist.

In Newtonian physics, we assume that we have an omniscient observer who knows where every mass in the universe is. We can then determine all gravitational forces and infer how a test particle would have moved if it hadn't been affected by gravity.

In relativity, we use the definition given in Dale's #2.

According to the Newtonian definition, the earth's surface is inertial, and the ISS is noninertial. According to the relativistic definition it's the other way around.

There is a discussion of this sort of thing in section 8.2 of my book Relativity for Poets http://lightandmatter.com/poets/ , which is free.

5. Mar 10, 2016

### hackhard

why is the earth frame inertial if it revolves around the sun?
and how is the sun frame inertial if revolves about center of milky way?

6. Mar 10, 2016

### Drakkith

Staff Emeritus
It's not an inertial frame. But we approximate it as an inertial frame most of the time unless accuracy requires us to do otherwise.

7. Mar 10, 2016

### A.T.

Think of a non rotating isolated planet. The surface is inertial in Newtonian mechanics, but non-inertial in GR. GR goes by what an accelerometer measures.

8. Mar 10, 2016

### hackhard

but we can approximate it as inertial frame only for earthly bodies

9. Mar 10, 2016

### CrazyNinja

True. If as @Drakkith says in #6, the earth being inertial is inaccurate for whatever it is that you are measuring, then take another body as an inertial frame. This body could be such that it plays a role similar to that which earth plays for what you called "earthly bodies".

10. Mar 10, 2016

### hackhard

IF
how will i know if my measurements are inacurate ?

11. Mar 10, 2016

### Staff: Mentor

This is why I use relativity's definition of inertial, which I described above.

12. Mar 10, 2016

### FactChecker

The application will determine how much accuracy you need. Here are a few assumptions that I would make:
1) If you are looking at the motion of things leaving the Earth, you definitely need the full Earth rotation and motion in the Solar System.
2) If you are looking at motion of things in orbit, you definitely need the full Earth rotation and probably can ignore motion in the Solar System.
3) If you are looking at long distance flights on Earth, you definitely need to consider the rotation of the Earth but can ignore the motion of the Earth in the Solar System
4) If you are only interested in short distance flights on Earth, you can probably assume that the Earth is not rotating or moving.
5) If you need incredible accuracy, you may need to consider more than indicated above.

Of course, there are always exceptions, but they are rare.

13. Mar 12, 2016

### David Lewis

If a significant gravitational field is present, the frame is non-inertial.

14. Mar 12, 2016

### hackhard

again , "significant" in comparison to what?

15. Mar 12, 2016

### David Lewis

Significant enough that you must take it into account to obtain your desired level of precision.

16. Mar 12, 2016

### FactChecker

For practical use, that is too strict. Most physics is done assuming that gravity is a force and does not prevent a coordinate system from being inertial. All the physics done before Einstein was like that. Until a person is dealing with relativity, he should do the same.

17. Mar 12, 2016

### David Lewis

You're correct. There are alternate definitions for the term non-inertial that, while they may obscure what is really going on, make problem analysis simpler.

18. Mar 12, 2016

### hackhard

so a frame can be taken to be inertial if pseodo forces in that frame are negligible compared to real forces
so centripetal acceleration of earth due to sun = 0.0059 m/s^2
so earth frame is inertial for motion of animals-- (pseudo force=40 kg * 0.0059 m/s^2)
so earth frame is not inertial for motion of sun-- (pseudo force= 2 × 10^30 kg * 0.0059 m/s^2)

Last edited: Mar 12, 2016
19. Mar 12, 2016

### FactChecker

I agree
Yes.
Is that right? I don't know where that is coming from. It looks like it is derived from the acceleration of the Earth's orbit around the Sun. That doesn't seem right to me. It should be related to the Earth's rotation rate of 360 deg/day and it would be different at the Equator versus the North Pole.
What do you mean?

20. Mar 12, 2016

### hackhard

AT north pole ,earth frame is inertial for motion of animals-- (pseudo force on animal=40 kg * 0.0059 m/s^2)
thus pseudo forces need not be added for laws of motion to be valid on animal( from earth frame )(AT north pole)

AT north pole , earth frame is not inertial for analyzing motion of sun-- (pseudo force on sun= 2 × 10^30 kg * 0.0059 m/s^2)
thus pseudo forces must be added for laws of motion to be valid on sun( from earth frame) (AT north pole)

Last edited: Mar 12, 2016