# What is an inertial frame of reference ?

1. Sep 6, 2007

### alvaros

what is an inertial frame of reference ?
Simple ?

2. Sep 6, 2007

### Danger

As simply put as I believe is possible, it's the immediate space-time co-oridinate in which the observer is not in motion. All measurements by the observer are in relation to that 'place'.

3. Sep 6, 2007

### meopemuk

An inertial frame of reference is a set of measuring devices, which moves with constant velocity along a straight line and without rotation.

Eugene.

4. Sep 6, 2007

### Staff: Mentor

It is a frame of reference in which Newton's laws of motion hold without needing to introduce fictitious forces such as "centrifugal force", "Coriolis force", etc.

5. Sep 7, 2007

### alvaros

Danger:
I dont understand. Note that this thread is post in the Classical Physics section. I suppose that, at the end, someone will refer to relativity. But, if you like, and its possible, lets talk as we are at 1900.
meopemuk:
rotation respect to what ?
jtbell:
What are fictitious forces ?

6. Sep 7, 2007

### meopemuk

The reference frame should not spin (rotate) around its own axis. In other words, looking from this frame, distant stars should not be seen in a circular motion (unlike we see it on Earth).

Actually, I don't think it is possible to give an unambiguous, exhausting, and rigorous definition of the inertial reference frame, simply because it is such a fundamental notion in physics, than it cannot be reduced to anything simpler. However, I don't think there is any controversy. We will all agree whether the frame is inertial or not when we see it.

Eugene.

7. Sep 7, 2007

### alvaros

meopemuk:
Again: rotate respect to what ?

Are you shure that distant stars ( the universe ) are not rotating ? Why ?

Do you know the paradox ( Newton ) of a bucket whith water. If the bucket rotates nothing happens but if the water rotates the surface of the water is like a "V". Newton said: the next book I will explain that... He never explained it.

Its Ok to say: inertial frame of reference ? ( frame, just geometry )
Shoudnt we talk about material frame of reference ?

8. Sep 7, 2007

### D H

Staff Emeritus
Forget about fictitious forces for a bit. Suppose you can see some object, and you know there no forces act on this object. If the object moves along a straight line with a constant speed you are in an inertial reference frame. This is Newton's first law of motion. You are not in an inertial reference frame if the object appears to undergo some kind of acceleration. Newton's first law essentially defines an inertial reference frame.

Newton's second law talks about what happens to objects that are acted upon by some force as seen from an inertial observer. The first law defines an "inertial reference frame" in terms of behavior. The second law similarly defines "force" in terms behavior.

Newton's second law is a very powerful device. It can be used to determine the state (location and velocity) of some object at any point in time based solely on state at some particular point in time and knowledge of the forces acting on the object. However, Newton's second law is valid only in an inertial frame. Because of its projective powers, it would be nice to extend this law to non-inertial frames.

Return again to the force-free object, but this time we observe it from a reference frame known to be non-inertial. The object will appear to accelerate. Dividing the observed acceleration by the mass yields something with units of force. By relating this force-like parameter to some attribute of our reference frame (its rotation or acceleration), we can use this force-like parameter as if it were a force in Newton's second law. The force isn't real (the object has zero external forces), so it is "fictitious".

9. Sep 7, 2007

### Loren Booda

Strictly speaking, can one extended (or more than one pointlike) masses comprise an inertial reference frame other than for a unique instant? In either case the objects interact gravitationally, causing immediate acceleration and thereafter non-inertial motion.

10. Sep 7, 2007

### meopemuk

The distant stars may be rotating and we may be rotating along with them, but we do not need to worry about that for doing physics here on Earth. The important thing is that (inertial) reference frames (in which distant stars look immobile) have very useful properties. In these reference frames the laws of physics have especially simple form (see DH's post above) and, most importantly, all these reference frames are equivalent to each other (the principle of relativity). These are good starting points for doing physics.

Eugene.

Last edited: Sep 7, 2007
11. Sep 7, 2007

### Staff: Mentor

To me, in the classical physics context, fictitious forces are "forces" that have no agent. That is, there is no object that is their ultimate "source." Gravity is not a contact force, but one can nevertheless say e.g. that gravitational force that makes an object fall, is exerted by the Earth, although indirectly. Likewise for electric and magnetic forces, although with these we also have to include time delays for propagation of electromagnetic waves etc.

But what exerts the "centrifugal force," "Coriolis force," and "transverse force" on an object in a rotating reference frame?

12. Sep 7, 2007

### NeoDevin

Wikipedia gives a pretty good description of inertial frame of reference:
And of fictitious forces:

13. Sep 7, 2007

### neelakash

Newton's first law says that whatever be the type of motion,you can always find an inertial frame from where the motion can be observed:no force no acceleration.
I will say that it is a frame where first law holds.

14. Sep 8, 2007

### HallsofIvy

You keep saying that- as if it meant something! Even in classical mechanics, velocity or speed is alway relative to something. Rotation, however, is acceleration and so is not relative.

15. Sep 8, 2007

### D H

Staff Emeritus
Rotation with respect to an inertial reference frame, of course. The test of an inertial frame is whether Newton's first two laws accurately describe the motion of objects as measured by an observer fixed to the frame. For example, distant quasars have unmeasurably small proper motion. A reference frame in which these distant quasars have a fixed position (e.g., the International Celestial Reference Frame ) is inertial. A reference frame in which these distant quasars appear to be rotating about some axis (e.g., an Earth-centered, Earth-Fixed Frame) is not inertial.

"Rotation with respect to what" most certainly does mean something. Moreover, acceleration is also relative. There is no such thing as an absolute reference frame. The acceleration of the Moon is quite different in a non-rotating, Earth-centered frame versus a non-rotating, solar system barycenter frame.

The transport theorem relates the derivative of any vector quantity $\boldsymbol q$ as seen by observers in two concentric reference frames $A$ and $B$:

$$\left(\frac{d\boldsymbol q}{dt}\right)_{\text{Frame A}} = \left(\frac{d\boldsymbol q}{dt}\right)_{\text{Frame B}} + \boldsymbol \omega_{A\to B}\times \boldsymbol q$$

16. Sep 8, 2007

### alvaros

Too many ideas to discuss but..

D.H:
This force means nothing and is not related to the mass(1). Tell about a real example of what you are saying.

jtbell:
The tension of the rope that holds the rotating mass.

HallsofIvy:
I agree. So there are absolute not rotating axes that are the same in all the universe and all inertial reference frames must not rotate respect to these axes. And thes axes dont need to refer to distant stars, but you need something material ( with mass ) to discover them. Do you agree ?

myself:
Id like to hear something about that. Dont you understand what Im saying in my poor english? Did you know the paradox ? Did you read anything on any book related/explaining this paradox ?

Thanks to all.

17. Sep 8, 2007

### nrqed

Yes, that's a smart way to put it!

18. Sep 8, 2007

### Staff: Mentor

That's the centripetal ("towards the center") force that causes the object to accelerate continuously towards the center of its circular path, in an inertial reference frame. It's very real.

I'm talking about the centrifugal ("away from the center") force that apparently pulls the object outwards, in a (non-inertial) rotating reference frame. The rope can't pull or push outwards on the object.

In a rotating reference frame such that the object is stationary, the (inward) tension in the rope and the (outward) centrifugal force combine to give a net force of zero. But the centrifugal force is purely an artifact of the rotating reference frame. In an inertial reference frame, there is no need to introduce a centrifugal force.

19. Sep 8, 2007

### D H

Staff Emeritus
That should have been "multiplying", not "dividing". The ratio of acceleration to mass obviously does not have units of force. The product does. Too much proposal work last week. The Coriolis force is the prototypical example of such a fictitious force.

We use the distant stars as to define our best estimate of what constitutes an inertial frame. We do this because the measurements are so incredibly precise. The International Celestial Reference Frame differs from J2000 by an incredibly small rotation rate, which differs from Mean-of-1950 by a slightly larger (by still very small) rotation rate. No earthly experiment could replicate the accuracy afforded by quasars.

20. Sep 9, 2007

### Danger

You guys are kind of weirding me out here. Maybe it's because of how inertial frames were explained to me way back, or maybe it's because I'm misinterpreting your posts, but it seems as if you're saying that I sitting here on my couch am in the same frame as the guy strolling along over my house in a 727.