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}} =<br /> \left(\frac{d\boldsymbol q}{dt}\right)_{\text{Frame B}} +<br /> \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]

 

[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

 

[D H]

First, the article was from www.economicexpert.com. Since when do economists give good advice on physics. Second, they are right, but not quite for the cited reason. We can only find an approximation to an inertial frame because of residual measurement error. Even if Newton's laws were true, we would still never be able to find a true inertial frame. A true inertial frame is an unreachable ideal. All of physics involves approximations at some point.

 

[alvaros]

D H:

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.

Are you applying centrifugal or centrifugal concepts to the person ?

Quote:
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.

You measure the motion of distant stars respect to a reference ( inertial ) . Then you say that the stars are the reference !

Observations of the remote stars (particularly quasars) is much, much more sensitive than anything we could do with masses

It can be more sensitive but the essentials you apply ( inertia of mass ) must be the same.

DaleSpam:

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.

And how do they work ? ( Lasers are not a valid answer here )

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

And you don't need distant stars.

jtbell:

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).

Yes, so centripetal/centrifugal are action/reaction. I never called them "fictitious"

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."

Confused ( me ). But:
This force is real ( the rope can break ) and the ball is what exert it. This is common sense.

 

[D H]

D H:

Are you applying centrifugal or centrifugal concepts to the person ?

Yes. Assume for the moment that the Earth is neither rotating about its own axis nor orbiting the Sun: In other words, assume the Earth is an inertial frame. The person is fixed with respect to the ground: her Earth-fixed velocity is zero. From your vantage point on the merry-go-round she is the one who is undergoing circular motion. not you. (You are sitting still on the merry-go-round, after all). In the merry-go-ground frame, her acceleration is \boldsymbol {\omega} \times (\boldsymbol {\omega} \times \boldsymbol r) = -\omega^2\boldsymbol r, where \boldsymbol{\omega} is the merry-go-rounds angular velocity wrt inertial and [\boldsymbol r is the vector from the center of the merry-go-round to the person. The product of the person's apparent acceleration and her mass is a fictitious force. If you use this fictitious force as if it were real, you would be able to say "F=ma" in the non-inertial merry-go-round frame.

You measure the motion of distant stars respect to a reference ( inertial ) . Then you say that the stars are the reference !

You measure the stars with whatever frame is handy (e.g., Earth-fixed) and then back out the inertial frame.

DaleSpam:

And how do they work ? ( Lasers are not a valid answer here )

Don't say that lasers are not a valid answer because ring laser gyros do indeed use lasers.

 

[Dale]

And how do they work ? ( Lasers are not a valid answer here )

They are really fascinating little pieces of work, and were really one of the first applications of MEMS technology. But lasers are used in all of the high quality ones and I don't see why they aren't a valid answer.

There are basically two kinds of transducers in one of these IMUs. The first kind is the one that measures linear accelerations. These range from small cheap things like a cantilever beam with a strain gauge to more sophisticated devices using lasers and mirrors to detect small deflections of a proof mass.

The second kind is the one that measures rotations. These range small and cheap micromachined gyros to the high-quality laser ring interferometers used in cruise missles.

Do you recall Einstein's famous thought-experiment where he essentially concluded that a man in a windowless room couldn't conduct an experiment to tell if a ball fell to the floor due to the fact that he was on a rocket or on the earth? Think of the accelerometer as the windowless room and the transducers as the experiments.

-Regards
Dale

 

[jtbell]

Confused ( me ).

You are confusing forces which act on the rope with forces that act on the ball. I am talking only about forces which act on the ball. When analyzing the motion of the ball, we must use only the forces that act on the ball.

In an inertial reference frame, the ball is continually accelerating towards the center of its circular path. We explain this as the effect of the centripetal force that the rope exerts on the ball. In this frame, this force has constant magnitude but continually changing direction.

In a reference frame which is rotating at the same rate as the ball, the ball is stationary. Therefore the net force on it (in this reference frame) must be zero, in order for Newton's First and Second Laws to hold (in this reference frame). The rope exerts a force on the ball, like in the inertial reference frame, except that in this frame, this force is constant in both magnitude and direction. In order to have a net force of zero on the ball, we must invoke a centrifugal force that acts on the ball, with equal magnitude and opposite direction.

But this centrifugal force is not exerted by any other object, so we call it "fictitious." It exists only in the rotating reference frame, whereas the force exerted by the rope on the ball exists in both reference frames.

 

[alvaros]

DH: ( talking about one person who is looking at the merry-go-rounds )
The product of the person's apparent acceleration and her mass is a fictitious force.

A force that doesn't agree with Newton 3rd law. Which are the pair action/reaction ?
This can be mathematically useful but hasnt any sense in phisics.

DaleSpam:
These range from small cheap things like a cantilever beam with a strain gauge to more sophisticated devices using lasers and mirrors to detect small deflections of a proof mass.

A proof mass.

]jtbell:
You are confusing forces which act on the rope with forces that act on the ball. I am talking only about forces which act on the ball. When analyzing the motion of the ball, we must use only the forces that act on the ball.

Forces always come in pairs and act on two different things.

In a reference frame which is rotating at the same rate as the ball, the ball is stationary. Therefore the net force on it (in this reference frame) must be zero, in order for Newton's First and Second Laws to hold (in this reference frame). The rope exerts a force on the ball, like in the inertial reference frame, except that in this frame, this force is constant in both magnitude and direction. In order to have a net force of zero on the ball, we must invoke a centrifugal force that acts on the ball, with equal magnitude and opposite direction.

But this centrifugal force is not exerted by any other object, so we call it "fictitious." It exists only in the rotating reference frame, whereas the force exerted by the rope on the ball exists in both reference frames.

Both forces ( centripetal and centrifugal ) exist in both scenarios. The rope can break, and if this happens the ball moves away ( in both scenarios )

 

[D H]

A force that doesn't agree with Newton 3rd law. Which are the pair action/reaction ?
This can be mathematically useful but hasnt any sense in phisics.

The whole point behind "fictitious" forces is that, while they are not real (hence the qualifier "fictitious") they are a very useful device, invented by physicists for use by physicists when dealing with non-inertial frames. You asked for an example of a fictitious force; I gave you one. Another example is the "Coriolis force", which meteorologists use as if it were quite real (they work in the rotating Earth-fixed frame).

A proof mass.

An accelerometer uses a proof mass. A gyroscope does not.

Forces always come in pairs and act on two different things.

No they don't. Fictitious forces do not. Moreover, Newton's third law is not universally true, even in the realm of classical physics (e.g., Biot-Savart law).

Both forces ( centripetal and centrifugal ) exist in both scenarios. The rope can break, and if this happens the ball moves away ( in both scenarios )

Suppose the string breaks. In the inertial frame, the ball simply moves in a straight line with the velocity it had at the moment the string broke. This is just Newton's first law.

Things are a lot trickier in the rotating frame. The ball's velocity is identically zero in the rotating frame up until the instant that string breaks. When the string breaks, the ball suddenly starts to move along a curved trajectory. How does this happen without some force (real or fictitious) acting on it?

 

[alvaros]

DH:
Ok, you are right, things happens because there are fictitious causes, a gyroscope does not need a big rotating mass and Newton's third law is not universally true ( as anybody knows and every book of physics says ).

 

[D H]

Alvaros, are you being intentionally thick? You asked, in post #5, "What are fictitious forces". Right before that, jtbell gave some specific examples of fictitious forces. Did you read this post? Did you try reading the wikipedia articles on inertial frames (link here), fictitious forces (link here), centrifugal forces (link here), or the Coriolis effect (link here)? Come back to us after reading these.

In non-inertial frames, things do appear to happen because of fictitious causes. That is the point of the fictitious forces. With them, we can use m\;d\boldsymbol{p}/dt = \sum \boldsymbol{F} to predict the state of some object. This makes the fictitious forces a very useful fiction.

 

[alvaros]

DH:
Come back to us after reading these.

Yes I am going to read those links before continuing talking about IFRs.
Thanks to all.

 

[alvaros]

All quotes from DH:

"What are fictitious forces". Right before that, jtbell gave some specific examples of fictitious forces.

Examples are not a definition. And less in this case where fictitious forces can be of two kinds: ones that distort the bodies ( real forces ) and others that dont.

Did you read this post?

I do read all posts.

But: What is an IFR ?

"An inertial frame of reference, or inertial reference frame, is one in which Newton's first and second laws of motion are valid." OK.

"The frame where exist fictitiuous forces" And what are fictitious forces ?
"A fictitious force, also called a pseudo force[1] or d'Alembert force[2], is an apparent force that acts on all masses in a non-inertial frame of reference ... " from Wiki
You can't include in your definition the concept you want to define !

Anyway what I wanted is to find a definition of IFR:

"An inertial frame of reference, or inertial reference frame, is one in which Newton's first and second laws of motion are valid."
And Newton's laws apply to objects that have mass, so you need a mass to have an IFR.
Do you agree ?

 

[D H]

Look, if an inertial frame is one in which Newton's first law of motion is valid, a non-inertial frame is a reference frame in which Newton's first law of motion is not valid. We can make Newton's second law of motion valid in some non-inertial frames by inventing forces that appear to act on objects. These forces are not real, hence the name "fictitious force". That is all that a fictitious force is: a fictional device that makes F=ma work in a non-inertial frame. By "work" I mean properly describe the behavior of objects as observed by someone whose state is fixed in a non-inertial frame.

Any two inertial frames are related by at most a constant velocity translation from one origin to the other and by a constant rotation from one set of axes to the other. You do not need a mass to have an inertial reference frame.

What do you mean by "so you need a mass to have an IFR"?

 

[alvaros]

Ill start another thread about this:
"Determine which reference frame is inertial"