What is an inertial frame of reference ?

[alvaros]

what is an inertial frame of reference ?
Simple ?

 

[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'.

 

[meopemuk]

what is an inertial frame of reference ?
Simple ?

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

Eugene.

 

[jtbell]

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.

 

[alvaros]

Danger:

it's the immediate space-time co-oridinate in which the observer is not in motion.

I don't 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, let's talk as we are at 1900.
meopemuk:

with constant velocity along a straight line and without rotation.

rotation respect to what ?
jtbell:

fictitious forces

What are fictitious forces ?

 

[meopemuk]

meopemuk:

rotation respect to what ?

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.

 

[alvaros]

meopemuk:

The reference frame should not spin (rotate) around its own axis

Again: rotate respect to what ?

distant stars should not be seen in a circular motion

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

Actually,... 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.

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 ?

 

[D H]

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".

 

[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.

 

[meopemuk]

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

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.

 

[jtbell]

What are fictitious forces ?

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?

 

[NeoDevin]

Wikipedia gives a pretty good description of inertial frame of reference:

An inertial frame of reference, or inertial reference frame, is one in which Newton's first and second laws of motion are valid. In other words, a reference frame that is neither rotating nor accelerated.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—i.e. in a straight line and at constant speed.

And of fictitious forces:

A fictitious force, also called a pseudo force or d'Alembert force, is an apparent force that acts on all masses in a non-inertial frame of reference such as a rotating reference frame. The force F does not arise from any physical interaction, but rather from the acceleration a of the non-inertial reference frame itself. Due to Newton's second law F = ma, fictitious forces are always proportional to the mass m being acted upon.

 

[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.

 

[HallsofIvy]

Again: rotate respect to what ?

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.

 

[D H]

rotation respect to what ?

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.

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.

"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 $B$:

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

 

[alvaros]

Too many ideas to discuss but..

D.H:

Dividing the observed acceleration by the mass(1) yields something with units of force.

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

jtbell:

But what exerts the "centrifugal force,"

The tension of the rope that holds the rotating mass.

HallsofIvy:

Rotation, ( ... ) is not relative.

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 don't need to refer to distant stars, but you need something material ( with mass ) to discover them. Do you agree ?

myself:

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.

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

Thanks to all.

 

[nrqed]

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?

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

 

[jtbell]

But what exerts the "centrifugal force,"

The tension of the rope that holds the rotating mass.

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.

 

[D H]

Too many ideas to discuss but..

D.H:

Dividing the observed acceleration by the mass yields something with units of force.

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

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.

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 don't need to refer to distant stars, but you need something material ( with mass ) to discover them. Do you agree ?

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.

 

[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.

 

[D H]

You are not in any reference frame. You have different coordinates in different reference frames, but you are still you regardless the reference frame I use as a basis for specifying your state. You are an invariant.

Consider the reference frame with origin at the center of your couch and axes rotating with the Earth. Your coordinates (when you are lazing around) are zero in that frame. The guy strolling along the aisle in a 727 flying over your house has a time-varying state in the Danger sofa frame. The guy in the airplane might use a 727-centered frame in lieu of the Danger sofa frame. Your sofa is moving at a good clip in the 727-centered frame.

Neither of these frames is inertial. The origin of the Danger sofa frame is accelerating with respect to inertial and the axes are rotating with respect to inertial. The same is true of the 727 frame.

 

[Danger]

Thanks, DH. I've had a few too many brews to be sure about this, but your explanation seems to imply that I was thinking of non-inertial frames. In my thinking, I'm at rest and everything else is moving relative to me. (At least, I hope that I'm at rest, because I'm too damned tired to move. )

 

[D H]

There is no such thing as a non-rotating reference frame after having a few too many brews.

 

[Danger]

:rofl::rofl:

:yuck:

 

[alvaros]

To me, in the classical physics context, fictitious forces are "forces" that have no agent.

If there is no agent there is no reaction ( Newton 3rd law ). I wouldn't call them "forces"

jtbell:

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.

Centripetal and centrifugal are action/reaction. Do you agree? If you dont, which are the reaction forces of centripetal/centrifugal ?

DH:

That should have been "multiplying", not "dividing".

Sorry, I just copy and paste...

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.

If I undestand, the rotation of distant stars has been measured. Respecto to what ?

But I like to get answers about these statements (if you are so kind in answering me):
1- There are absolute not rotating axes
2- All inertial reference frames must not rotate respect to these axes
3- you need something material ( with mass ) to discover them

( 1 ) ( 2 ) Any inertial reference frame ( IRF ) can have a movement of translation respect to another one, but it can't have a rotation respect to another one.
( 3 ) The mass is what tell us if the frame is rotating or not.

 

[D H]

If there is no agent there is no reaction ( Newton 3rd law ). I wouldn't call them "forces"

These things (e.g. Coriolis "force") have units of force. They are not real, which why we call them fictitious. Very useful fictions.

Centripetal and centrifugal are action/reaction. Do you agree?

No. Example: You are on a merry-go-round. You observe someone standing still on the ground outside the merry-go-round. You see that person as accelerating. There is no real centripetal force (the person is standing still). The apparent acceleration results solely because you are observing the person from the vantage point of a rotating frame.

If I undestand, the rotation of distant stars has been measured. Respecto to what ?

With respect to inertial. The apparent motion of the remote stars can be separated into "proper" and "improper" motion. Causes of improper motion include diurnal rotation, nutation, precession, and parallax. The treatment is statistical. The end result is our best guess regarding what constitutes an inertial frame.

But I like to get answers about these statements (if you are so kind in answering me):
1- There are absolute not rotating axes
2- All inertial reference frames must not rotate respect to these axes
3- you need something material ( with mass ) to discover them

In order,
1- There are absolute not rotating axes
Inertial frames exist in classical mechanics. Any two inertial frames are related by a fixed rotation and by a constant velocity displacement. Call that absolute fixed rotation absolute if you so wish.

2- All inertial reference frames must not rotate respect to these axes
Correct.

3 - you need something material ( with mass ) to discover them
Incorrect. Observations of the remote stars (particularly quasars) is much, much more sensitive than anything we could do with masses. No mass is needed. Just a very fancy telescope.

 

[Dale]

I have enjoyed all of the physics comments. Here is an engineer comment:

An inertial reference frame is one in which an ideal accelerometer (6 degree of freedom kind) at rest in the frame would not measure any acceleration.

-Regards
Dale

 

[D H]

What if the frame in which the accelerometer is at rest is rotating with the axis of rotation passing through the accelerometer? You better add an ideal rate gyro to the ideal accelerometer.

 

[Dale]

The 6 degree of freedom accelerometers are the kind used in inertial guidance systems. They measure acceleration on 3 axes and rotation about 3 axes. So they would detect the frame you describe as being non-inertial.

Here is an example describing the kind that are used in the Wii ( http://www.analog.com/en/content/0,2886,998%255F%255F8078%255F0,00.html )

-Regards
Dale

 

[D H]

I missed the 6DOF. We call those thingies IMUs (inertial measurement units); they comprise a 3-axis accelerometer and a 3-axis gryo. Calling them accelerometers is a bit of a misnomer, isn't it?

 

[Dale]

Ahh, you are quite right. I didn't know the term "IMU" so I always specified the degrees of freedom. IMU is much more convenient and clear.

Anyway, if an ideal IMU is at rest and reads 0, the frame is inertial (according to any decent engineer).

-Thanks
Dale

 

[jtbell]

Centripetal and centrifugal are action/reaction. Do you agree?

No, at least not in the sense of "centrifugal force" that people usually mean.

An action/reaction pair of forces in the sense of Newton's Third Law can always be described as "the force that object A exerts on object B" and "the force that object B exerts on object A."

In the case of a ball whirling around on a rope, if the "action" force is "the force that the rope exerts on the ball" (centripetal), then the "reaction" force is "the force that the ball exerts on the rope." This force is indeed "centrifugal" (outwards from the center) but it acts on the rope, not on the ball, and it has a definite agent (the ball).

In a rotating reference frame in which the ball is stationary, we have to include a centrifugal force on the ball in order to counteract the centripetal force exerted by the rope and make the net force on the ball equal to zero. This centrifugal force has no agent (what could possibly exert it?), and is therefore "fictitious."

 

[rewebster]

what is an inertial frame of reference ?
Simple ?

Isn't it a way to differentiate Newtonian and 'relativity' motions?

"The frame concept is at the core of the questions dealing how the apparent classical mechanics of particular inertial frame relates to the general theories of the universe and spacetime"

http://www.economicexpert.com/a/Inertial:frame:of:reference.html

 

[D H]

The cited article talks about Newtonian relativity, which is fine; this is embedded in Newton's first law (to be pedantic, its Galilean relativity, not Newtonian). But please don't invoke special relativity. The OP is having a hard enough time with the classical concept.

 

[rewebster]

The part that I found most interesting to the thread was:

"Frames of reference are purely theoretical, because gravitational force (and thus acceleration) exists everywhere in the known universe."

----

as jtbell in post 11 (and 32) may be referring to