# Inertial frame of Reference?

#### gztiger

I am confuse of what is inertial frame of reference.
Can someone explain that to me?
I need a clear explanation starting from the beginning to the end, and if possible, give me some set of example.

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anyt

#### Bob_for_short

It is a reference frame that stays always still or moves at a constant velocity V.

#### jonjacson

there are some threads talking about non inertial reference frames, you can search them.

Otherwise, I think that an inertial frame is a frame where second newton law holds true, if you make measures and the results given by F=ma are false, that means that you are on a non inertial frame (like the earth, because it is rotating).

The key of the question (I think) is that F=ma says that to every acceleration corresponds a force, but if you are in an accelerated frame (non inercial) you "see" accelerations that does not correspond to any real force like gravity, electricity and so on, they only correspond to your state or motion.

So If you want to use newton laws you must introduce the "ficticious" forces into the F=ma , and then this equation will be lawful in the non inertial frame, verily they are not real forces, but they describe the new accelerations due to the movement of the non inercial frame.

In the earth you have to introduce this ficticious forces to the newton equation:

-translation force (you feel it when a train starts a travel , is not a true force, but mathly is useful to explain the acceleration that you feel, if you are into the train(so on a non inertial frame)).

-centrifugal force (you feel it when you are sitted into your car and you are driving into a curve, you feel acceleration, another time is not a real force, but in your frame it makes the same as it was a real force, so you have to insert this term into the equation).

-coriolis, and azimuthal forces are more tricky to explain.

#### HallsofIvy

Homework Helper
there are some threads talking about non inertial reference frames, you can search them.

Otherwise, I think that an inertial frame is a frame where second newton law holds true, if you make measures and the results given by F=ma are false, that means that you are on a non inertial frame (like the earth, because it is rotating).

The key of the question (I think) is that F=ma says that to every acceleration corresponds a force, but if you are in an accelerated frame (non inercial) you "see" accelerations that does not correspond to any real force like gravity, electricity and so on, they only correspond to your state or motion.
But what are "real forces"? If I feel a force on me, how do I decide, in my frame of reference, whether it is a "real" force or not? What experiments can I run, in a closed laboratory, say, to determine whether my rest frame is inertial or not?

So If you want to use newton laws you must introduce the "ficticious" forces into the F=ma , and then this equation will be lawful in the non inertial frame, verily they are not real forces, but they describe the new accelerations due to the movement of the non inercial frame.

In the earth you have to introduce this ficticious forces to the newton equation:

-translation force (you feel it when a train starts a travel , is not a true force, but mathly is useful to explain the acceleration that you feel, if you are into the train(so on a non inertial frame)).

-centrifugal force (you feel it when you are sitted into your car and you are driving into a curve, you feel acceleration, another time is not a real force, but in your frame it makes the same as it was a real force, so you have to insert this term into the equation).

-coriolis, and azimuthal forces are more tricky to explain.

#### jonjacson

But what are "real forces"? If I feel a force on me, how do I decide, in my frame of reference, whether it is a "real" force or not? What experiments can I run, in a closed laboratory, say, to determine whether my rest frame is inertial or not?
You can't , that is the equivalence principle from Einstein, acceleration due to gravity is not different of any other acceleration of the same magnitude, but in the Eart sciences you use that terminology.

#### A.T.

But what are "real forces"?
Those which obey Newtons 3rd law?
If I feel a force on me, how do I decide, in my frame of reference, whether it is a "real" force or not?
If you "feel" it is a "real" force because fictional forces accelerate everything equally, so you don't feel them?
What experiments can I run, in a closed laboratory, say, to determine whether my rest frame is inertial or not?
Shine a laser, and see if the beam bends?

#### jonjacson

Those which obey Newtons 3rd law?

If you "feel" it is a "real" force because fictional forces accelerate everything equally, so you don't feel them?

Shine a laser, and see if the beam bends?
About the second point, if we have these two situations:

-you are inside an elevator in a gravitational field

-you are inside the elevator, and it is accelerated by a rocket at 9,8 m/s2 (logically without gravity)

If you can't make measures from the outside of the elevator ¿can you feel any difference?

#### TurtleMeister

jonjacson said:
HallsofIvy said:
But what are "real forces"? If I feel a force on me, how do I decide, in my frame of reference, whether it is a "real" force or not? What experiments can I run, in a closed laboratory, say, to determine whether my rest frame is inertial or not?
You can't , that is the equivalence principle from Einstein, acceleration due to gravity is not different of any other acceleration of the same magnitude, but in the Eart sciences you use that terminology.
But you can determine, through experimentation, if a force is due to gravity or acceleration. Example: Two plum lines separated by a distance will not be parallel in the case of gravity, but they will be in the case of linear acceleration. I agree with A.T. Real forces are those that obey Newtons laws. However, it really depends on how precise you need to be. Your experiments may show that all forces and motions obey Newtons laws. But upon more precise measurements you will discover that they do not. There are no real perfect inertial frames. Or, maybe there are. We just don't know where they're at.

#### A.T.

About the second point, if we have these two situations:
-you are inside an elevator in a gravitational field
-you are inside the elevator, and it is accelerated by a rocket at 9,8 m/s2 (logically without gravity)
If you can't make measures from the outside of the elevator ¿can you feel any difference?
No, that's why both elevators are non-inertial in relativity.

#### jonjacson

But you can determine, through experimentation, if a force is due to gravity or acceleration. Example: Two plum lines separated by a distance will not be parallel in the case of gravity, but they will be in the case of linear acceleration. I agree with A.T. Real forces are those that obey Newtons laws. However, it really depends on how precise you need to be. Your experiments may show that all forces and motions obey Newtons laws. But upon more precise measurements you will discover that they do not. There are no real perfect inertial frames. Or, maybe there are. We just don't know where they're at.
-In the "force due to acceleration" picture , if you would put a mass sufficiently far away , the lines of force would be almost parallel, so ¿could you distinguish it from a force due to acceleartion?.

Perhaps the solution is what you say about what level of precision we want, but I suppose that practically it would be very difficult to measure that.

-

No, that's why both elevators are non-inertial in relativity.
But you said that you can "feel" real forces, because fictious forces accelerate everything equally , and I understand from this, that you can't "feel" ficticious forces , but that is not clear because in a curve into a car you "feel" the centrifugal force.

-------

I don't know where will finish this debate, but it is interesting and I appreciate your replies.

#### TurtleMeister

gztiger said:
I am confuse of what is inertial frame of reference.
Can someone explain that to me?
I need a clear explanation starting from the beginning to the end, and if possible, give me some set of example.
You may find this 4-part video helpful. It assumes no previous knowlege of inertial frames.
jonjacson said:
-In the "force due to acceleration" picture , if you would put a mass sufficiently far away , the lines of force would be almost parallel, so ¿could you distinguish it from a force due to acceleration?.

Perhaps the solution is what you say about what level of precision we want, but I suppose that practically it would be very difficult to measure that.
Yes, it depends on what the precision requirements are. There are also other ways to detect whether a force is due to gravity or acceleration. The force of gravity decreases according to the square of the distance. If you're standing on the 1st floor of a high rise building, then you will have more force than if you were standing on the top floor. However, if the building were being accelerated by a rocket then the force would be equal on all floors. And there are tidal forces associated with gravity, although those would be even more difficult to detect.

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#### A.T.

But you said that you can "feel" real forces, because fictious forces accelerate everything equally , and I understand from this, that you can't "feel" ficticious forces , but that is not clear because in a curve into a car you "feel" the centrifugal force.
No you don't feel the centrifugal force. It accelerates every part of your body uniformly so it creates no stresses that you could sense. What you eventually feel is the centripetal force applied to your face by the side window. That is a real force.

#### jonjacson

You may find this 4-part video helpful. It assumes no previous knowlege of inertial frames.

Yes, it depends on what the precision requirements are. There are also other ways to detect whether a force is due to gravity or acceleration. The force of gravity decreases according to the square of the distance. If you're standing on the 1st floor of a high rise building, then you will have more force than if you were standing on the top floor. However, if the building were being accelerated by a rocket then the force would be equal on all floors. And there are tidal forces associated with gravity, although those would be even more difficult to detect.
Thanks for the videos.

No you don't feel the centrifugal force. It accelerates every part of your body uniformly so it creates no stresses that you could sense. What you eventually feel is the centripetal force applied to your face by the side window. That is a real force.
In the case of an accelerometer, you have x as function of the acceleration of the noninertial frame ¿how could you explain that ?

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#### D H

Staff Emeritus
The centrifugal force at some point is $-m\boldsymbol{\Omega}\times(\boldsymbol {\Omega} \times \mathbf r)$. This is not a uniform force.