What is an inertial frame of reference ?

[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"