# How do you tell you are not in inertial frame of reference

1. Mar 27, 2009

### the-genius

While explaining about inertial and non-inertial frame of reference, people give this example--
http://www.phys.unsw.edu.au/einsteinlight/jw/module1_Inertial.htm
if you don't wish to follow the link, here is a simple explanation--->
there are two person and a rotating disk. Person A is in rotating disk and person B outside.
Both will see each other revolving around. But when person A throws a ball towards the rotating person B it won't straight but curving round to meet Person B, but however If person B throws a ball then it goes straight.

I think the flaw here is asuming that the force that provides centripetal force to the Person A,(may be frictional force here), is applied to the Person only but not the ball. What if the ball was rolled out on the disk and it had les assume: infinite friction (so that, when the ball is just placed on the side of person A, it won't shoot out of the disk, due to the same friction that holds person A), then the ball will go straight for person A, But curving for person B. Now, can you say Person A is in inertial Frame of reference.

2. Mar 27, 2009

### Al68

Nope, because the friction is a force acting on the ball, then. If the frame were inertial, the ball would travel in a straight line with no force acting on it. Because F=ma in an inertial frame. And in your example, the acceleration of the ball observed by the inertial observer (outside the disk) would be proportional to the frictional force acting on the ball. Again because F=ma in an inertial frame.

An inertial frame is identified by the fact that F=ma, that's why the ball will travel in a straight line as observed from an inertial frame, if there is no force acting on it.

3. Mar 27, 2009

### the-genius

How does person A knows (by mere looking) that the ball is going straight due to frictional force but not because Its in inertial frame. I think he will be free to say anything.

4. Mar 27, 2009

### Al68

Well, he might have to make other observations to determine he is not at rest in an inertial frame, if he can't verify that the ball has a force acting on it. But notice how easy that would be. There will be "fictional" forces acting on everything that is not tied down, including any celestial object he observes.

It's important to note that the very definition of an inertial frame is one in which F=ma and there are no "fictional" forces acting on any objects.

5. Mar 27, 2009

### the-genius

I am asking the very question, what experiment would he carry out to test whether he is in inertial frame or not.. (but remember that if he is provided a fictional force so should every objects he will experiment with.)

6. Mar 28, 2009

### Al68

He could release a ball into freefall and see if F=ma (ball travels in straight line when it's not in contact with anything).

Or he could notice that person B is going around him in circles.

Or he could measure the force acting on an object attached to the disk indirectly with a spring.

There are many specific ways to tell, but they are all based on the fact that F=ma in an inertial frame. Any experiment that can measure force applied and relative velocity of an object will work. Of course it's easier to just release an object into freefall with zero applied force and measure its velocity over time.

In an inertial frame, an object in freefall will travel in a straight line with constant speed.

7. Mar 28, 2009

### atyy

In a noninertial frame, you can ascribe accelerations to forces (from material bodies), but not all forces will be in a third law pair, ie. the second law will work, but the third law will not.

8. Mar 28, 2009

### the-genius

Al68, if you are in a box free-falling (acclerating with g) on earth, would you consider this box, a inertial frame of refernce?
If no, then why not? If you leave a ball ball here, it will obey F=ma (at leat for you). If you throw it, it will move in constant line with respect to you, following Newtons law. How, then it can't be inertial frame of reference?

9. Mar 28, 2009

### Staff: Mentor

Yes, in the limit of a small enough box that tidal effects are not noticeable. This line of thought led Einstein to General Relativity, in which gravitation is not a force.

10. Mar 28, 2009

### Al68

Yes, the box would be an inertial reference frame (approximately, disregarding tidal effects like jtbell pointed out).

An observer stationary on earth's surface is non-inertial, with a 1 G proper acceleration. That's why we feel the force of the ground pushing up against our feet just like we would in a ship in deep space accelerating at 1 G. And the relative acceleration of objects in freefall further shows that earth's surface is not an inertial frame.

That's how modern physics treats it. Classical physics treated an observer on earth's surface as (approximately) inertial, and gravity as an applied force. In which case, the F in F=ma was attributed to the "force" of gravity, and accounted for a freefalling objects relative acceleration. For our purposes in this thread, we could use either modern or classical physics and the results would be the same.

Last edited by a moderator: Mar 28, 2009
11. Mar 28, 2009

### Staff: Mentor

He can read an accelerometer. If it reads 0 then it is inertial, otherwise it is non-inertial.

12. Mar 28, 2009

### atyy

One thing that may be helpful is to distinguish between local and global inertial frames. In special relativity, global Lorentz inertial frames exist. The Rindler frame of a constantly accelerated observer is not a global Lorentz inertial frame, but there are local Lorentz inertial frames almost everywhere in the Rindler frame. "Inertial frame" usually means "global inertial frame".

13. Mar 28, 2009

### the-genius

How do you distinguish global and local inertial frames, atyy, please please explain in your own words (I wouldn't like a link to a lengthy explanation with difficult maths, I just need the concept)

14. Mar 28, 2009

### Staff: Mentor

A global inertial frame is one where any accelerometer at rest anywhere will read 0.

15. Mar 28, 2009

### Fredrik

Staff Emeritus
What DaleSpam said (twice).

I'm just going to add that the motion of an accelerometer that reads zero doesn't define an inertial frame by itself. It defines the time axis. You need to have a clock moving with the accelerometer in order to assign coordinates to events on the time axis, and then you have to use the usual synchronization procedure to assign coordinates to events that aren't on the time axis. The basic idea is that if light is emitted in the positive x direction at (-T,0), then reflected somewhere, and finally detected at (T,0), the coordinates of the reflection event are (0,cT).

Last edited: Mar 28, 2009
16. Mar 28, 2009

### Staff: Mentor

Good point. It only defines an inertial observer. Thanks for the clarification about how to extend that to an inertial frame.

17. Mar 28, 2009

### D H

Staff Emeritus
Emphasis mine ...
An accelerometer located at the center of mass of a free-falling spacecraft (which is the ideal location for an accelerometer) will measure zero whether or not the spacecraft is rotating. Just because the accelerometer reads zero does not mean the frame is inertial. It means the accelerometer is free-falling, and nothing else.

A reference frame comprises an origin and a set of axes. To determine whether a reference frame is inertial you also need to know whether the frame is rotating. Fortunately, instruments exist (e.g., rate-based gyros) to do just that.

18. Mar 28, 2009

### Cantab Morgan

I'd like to point out that it's Newton's third law that brings consistency to our ability to detect whether we're in an inertial reference frame.

If you wonder whether you're in an inertial reference frame, and you witness an accelerating object, then you need a way -- at least in principle -- to tell whether the object is accelerating because of a real force or because of a "fictitious force."

If it's a real force, then the third law requires there to be some other object out there that's experiencing the equal and opposite force.

19. Mar 28, 2009

### Naty1

DH posted:
Hey fantastic....I knew rate based gyros do a superior job as steering instruments aboard boats in rough seas....but I did not know that the "rate" was measuring accleration....My own automatic steering is controlled by a traditional gyro compass (no rate feature) and often I can do a better job manually by anticipating approaching waves...but its tiring....

20. Mar 28, 2009

### D H

Staff Emeritus
It's not. Rate-based gyros measure angular velocity, not acceleration.