Is a point (x distance from earth) inertial frame ?

[ManishR]

me and my friend were arguing (like always) about inertial frame ?

to sum up i m just asking a straightforward question ?

let say (for simplicity) there is just Earth and an other object in whole universe. a point whose distance from Earth is x. and dx/dt = 0.

now is that point (which can act as origin of frame) inertial frame ?


if u can spare more 5 min can u please define inertial frame ?

thanks

 

[Dale]

A reference frame is a coordinate system. A point is not a coordinate system.

Once you have a coordinate system, whether or not you consider it to be inertial depends on if you are using relativity or Newtonian mechanics, and if your coordinate system of interest covers only a small region of spacetime or the entire spacetime.

 

[ManishR]

by that i mean
a frame of reference whose origin is that point.
and i indicated that in question (however i am for not being clear) .

i have not study relativity yet so tell me in Newtonian mechanics.

 

[Dale]

Right, but it takes more than an origin to define a coordinate system. Are the axes orthonormal and cartesian, are they rotating or accelerating in any way? Etc. You need to define your entire coordinate system, not just specify a point. It is possible to make an inertial reference frame and a non-inertial frame which share the same origin.

In Newtonian mechanics an inertial reference frame is one in which Newton's three laws hold (in their standard form) as well as Newton's law of gravitation. Once you have one inertial frame, all others are related to that one via translations in space and time, spatial rotations, and/or Galilean boosts.

 

[ManishR]

Right, but it takes more than an origin to define a coordinate system. Are the axes orthonormal and cartesian, are they rotating or accelerating in any way? Etc. You need to define your entire coordinate system, not just specify a point. It is possible to make an inertial reference frame and a non-inertial frame which share the same origin.

again i apologize, its Cartesian, all three axis are perpendicular to each other and the point is origin of the frame.

In Newtonian mechanics an inertial reference frame is one in which Newton's three laws hold (in their standard form) as well as Newton's law of gravitation. Once you have one inertial frame, all others are related to that one via translations in space and time, spatial rotations, and/or boosts.

i never understood the meaning of the line "laws hold".

let me give u my definition of inertial frame (Cartesian) in Newtonian mechanics. and correct me if i am wrong.

consider (in 1D universe, for simplicity) an object with mass m and the object is acted by fundamental force (gravitational ) f.
now s would be inertial if
acceleration between frame and the object = f/m.
or else it would be non inertial.

 

[Dale]

i never understood the meaning of the line "laws hold".

It means that the following equations are true in terms of the coordinates, x:
$$\Sigma \mathbf f=m\frac{d^2 \mathbf x}{dt^2}$$
$$\mathbf f_{ab}=-\mathbf f_{ba}$$
$$\mathbf f_G=\frac{G m_a m_b}{|\mathbf x_a-\mathbf x_b|^3}(\mathbf x_a-\mathbf x_b)$$

s would be inertial if
acceleration between frame and the object = f/m.
or else it would be non inertial.

Yes. That works, assuming f follows the gravitational force law given above.

 

[ManishR]

so it means Earth is non inertial frame. it means the point (i mean the frame), is non inertial .
am i right ?

 

[Dale]

it means the point (i mean the frame), is non inertial

Which of the above equations does not hold in that frame?

 

[ManishR]

Which of the above equations does not hold in that frame?

i am sorry but i really don't understand the question.to define Newtonian force u have to use inertial frame. it means

Newtonian force = ma where a is the acceleration from object of mass m such as a = f/m.
so Newton second law say
Newtonian force = fundamental force on that object

so
u can't use that point as frame of reference (for a in ma) because there is fundamental force on it.
so u can't use the first equation.

 

[Dale]

i am sorry but i really don't understand the question.

I am just trying to help you work through the question. As we have discussed, an inertial frame is one in which Newton's laws hold. If a frame is non-inertial then one or more of Newton's laws must not hold, meaning that one of the above equations is false.

Once you can identify which equation does not hold and why it does not hold then you can convince your friend, otherwise the argument will continue.

to define Newtonian force u have to use inertial frame

Not really, you can measure forces (except for gravity) with a force transducer of one kind or another. That doesn't even require any coordinate system at all. But that is probably a subtle point that you don't need to go into.

u can't use that point as frame of reference (for a in ma) because there is fundamental force on it.
so u can't use the first equation.

Exactly. So, in this frame there is an object at the origin (the point mass) which is experiencing a non-zero gravitational force (given by the third equation) but which is not experiencing an acceleration (given by the first equation). Therefore, the first equation does not hold in this reference frame and therefore the reference frame is non-inertial according to the definition.

 

[ManishR]

not really, you can measure forces (except for gravity) with a force transducer of one kind or another. That doesn't even require any coordinate system at all. But that is probably a subtle point that you don't need to go into.

i am taking about Newtonian force not fundamental force, for Newtonian u need inertial frame.

Exactly. So, in this frame there is an object at the origin (the point mass) which is experiencing a non-zero gravitational force (given by the third equation) but which is not experiencing an acceleration (given by the first equation). Therefore, the first equation does not hold in this reference frame and therefore the reference frame is non-inertial according to the definition.

there does not has to be a point mass at the point to make it non inertial.
it is non inertial because Earth is non inertial. since a frame whose acceleration from a non inertial frame is zero, is also a non inertial frame.

earth is non inertial because there is gravity acting on it. (if there were only Earth nothing else => no gravity => its inertial)
acceleration of that point from Earth is zero so that point is also non inertial.
thats it.

I am just trying to help you work through the question. As we have discussed, an inertial frame is one in which Newton's laws hold. If a frame is non-inertial then one or more of Newton's laws must not hold, meaning that one of the above equations is false.

Once you can identify which equation does not hold and why it does not hold then you can convince your friend, otherwise the argument will continue.

i appreciate ur time and help.
but Newton specifically said to use Newtons laws u have to use inertial frame otherwise it won't work.

so the point frame is non inertial it means Newtons laws won't hold.
but its not like this
Newton laws does not hold it means the point frame is non inertial.

 

[D H]

i am taking about Newtonian force not fundamental force, for Newtonian u need inertial frame.

No, you don't. Force is an undefined term in Newtonian mechanics, in exactly the same sense that points, lines, and planes are undefined terms in Euclidean geometry. Forces (real forces) are something that exist outside of the reference frame. Newton's first law in a sense defines an inertial frame: All particles that are subject to zero net force will move at a constant velocity in an inertial frame. If a particle subject to zero net force is not moving at a constant velocity in some frame of reference then that frame is not inertial.

 

[Dale]

i am taking about Newtonian force not fundamental force, for Newtonian u need inertial frame.

I don't understand this distinction you are trying to make. What is a "Newtonian force" as opposed to a "fundamental force" in your usage? I know of "real forces" and "fictitious forces". Perhaps you mean "fundamental" = "real" and "Newtonian" = "fictitious".

there does not has to be a point mass at the point to make it non inertial.
it is non inertial because Earth is non inertial.

If there is no other mass besides the Earth then the Earth is inertial since there is no net force acting on it.

earth is non inertial because there is gravity acting on it. (if there were only Earth nothing else => no gravity => its inertial)
acceleration of that point from Earth is zero so that point is also non inertial.
thats it.

Where is the gravity coming from? You said in your OP that there was only the Earth and the point (which I incorrectly assumed was a point mass), so if the point is not a mass then there is no net gravitational force acting on the earth.

 

[ManishR]

No, you don't. Force is an undefined term in Newtonian mechanics, in exactly the same sense that points, lines, and planes are undefined terms in Euclidean geometry. Forces (real forces) are something that exist outside of the reference frame. Newton's first law in a sense defines an inertial frame: All particles that are subject to zero net force will move at a constant velocity in an inertial frame. If a particle subject to zero net force is not moving at a constant velocity in some frame of reference then that frame is not inertial.

actually he did, even if he did not, does not mean that force (or point,lines and planes) can't be defined after the invention of Newton mechanics (or euclidean geometry).

I don't understand this distinction you are trying to make. What is a "Newtonian force" as opposed to a "fundamental force" in your usage? I know of "real forces" and "fictitious forces". Perhaps you mean "fundamental" = "real" and "Newtonian" = "fictitious".

Newtonian Force = ma
(where a is acceleration between an inertial frame and that object of mass m)
Fundamental force is gravitational or electric etc.
so in this fundamental force = G(m1)(m2)/r^2 where m1 is mass of the another object and m2 is mass of Earth [excuse my laziness]

so second law says
Newtonian force of mass m = sum of fundamental forces on that object.

If there is no other mass besides the Earth then the Earth is inertial since there is no net force acting on it.
Where is the gravity coming from? You said in your OP that there was only the Earth and the point (which I incorrectly assumed was a point mass), so if the point is not a mass then there is no net gravitational force acting on the earth

please look at the OP again i have considered three things earth, the point and another object.
i have also indicated in previous post that if there is only earth, fundamental force would be zero.

 

[Dale]

Look ManishR, I cannot follow half of what you are saying. Every time you post I find that I misunderstood yet another important detail. I think there is a bad language barrier.

It seems that you know enough physics (although it is hard to tell with the communication difficulties and I don't particularly want to try to figure out what you meant in your last post), and if you are not able to convince your friend it is probably due to a language barrier also.

 

[ManishR]

ya i know that's why asked a simple and straightforward question. and i got the answer right which u confirm as well.

thanks for the help and time.

 

[D H]

actually he did, even if he did not, does not mean that force (or point,lines and planes) can't be defined after the invention of Newton mechanics (or euclidean geometry).

Actually, he didn't. Explain his first law otherwise.

Aside: "Undefined term" has a special meaning in mathematics.

 

[ManishR]

first law is nothing more than a special case of second law (Newtonian force = fundamental force).
consider an object of mass m.
first laws says
if vector sum of fundamental forces = 0
=> Newtonian force = 0
=> it has zero acceleration with respect to the inertial frame of reference.
=> and it will change its velocity only when it is experienced by an fundamental force.

 

[D H]

The interpretation you suggested, that the first law is a special case of the second, is not the sign of a brilliant mind. Newton was one of the smartest people of all times. Newton had something special in mind with his first law. It is much more than a special case of the second law. It sets the framework for the second law. The modern interpretation is that the first law defines the concept of an inertial frame of reference.

 

[ManishR]

The interpretation you suggested, that the first law is a special case of the second, is not the sign of a brilliant mind. Newton was one of the smartest people of all times. Newton had something special in mind with his first law. It is much more than a special case of the second law. It sets the framework for the second law. The modern interpretation is that the first law defines the concept of an inertial frame of reference.

may be u r right. but the thing is i have not been able to see a problem with this version of Newtons laws and if i see a problem, i will change it accordingly like i have changed many times (simple as that).

where is the fun if u don't use ur own physics. of course sometime u will be right and most of time u will be wrong. so what.

 

[rcgldr]

The simple explanation for an inertial frame is one that isn't accelerating (if it's not accelerating, then Newton's laws hold within that frame of reference).

 

[ManishR]

The simple explanation for an inertial frame is one that isn't accelerating (if it's not accelerating, then Newton's laws hold within that frame of reference).

acceleration with respect to what ?
acceleration need two point, one is the origin of inertial frame but where is the second point.

 

[rcgldr]

acceleration with respect to what?

In a frame of reference where gravity isn't present, or where the amount of gravity from external sources is known, then acceleration can be detected without requiring an external reference point. I was trying to use a simple explanation. In an inertial frame, all objects move at constant velocity unless acted upon by an external force (gravity would be considered an external force).

http://en.wikipedia.org/wiki/Inertial_frame_of_reference

 

[D H]

The simple explanation for an inertial frame is one that isn't accelerating (if it's not accelerating, then Newton's laws hold within that frame of reference).

Close.

An inertial reference frame is one whose origin is not accelerating with respect to some other inertial frame and whose axes are not rotating with respect to some other inertial frame.

 

[ManishR]

An inertial reference frame is one whose origin is not accelerating with respect to some other inertial frame and whose axes are not rotating with respect to some other inertial frame.

ya that's true.but you are supposed to define inertial frame without using inertial frame.

i gave u the definition.

 

[D H]

You did? Where?

And do stop using text speech. It is against the rules of this forum.

 

[ManishR]

You did? Where?

consider two object of mass $$m{}_{a}$$ & $$m{}_{b}$$ and distance between
them $$r{}_{0}$$.

now inertial frame will be $$\vec{r}{}_{a}$$ from $$m{}_{a}$$ if

$$m{}_{a}$$$$\frac{d^{2}}{dt^{2}}\vec{r_{a}}$$ = $$G\frac{m_{a}m_{b}}{r_{0}^{2}}\hat{n}$$
and

$$m{}_{a}\frac{d^{2}}{dt^{2}}\vec{r_{a}}= -m_{b}\frac{d^{2}}{dt^{2}}\vec{r_{b}}$$

And do stop using text speech. It is against the rules of this forum.

sorry for that i did not know.