What's the difference between an inertial frame....

[physics user1]

And a cartesian axis system in physics?
I thought about that and my answer is that a cartesian axis system is the same as a inertial frame of reference, is that true?

 

[phinds]

And a cartesian axis system in physics?
I thought about that and my answer is that a cartesian axis system is the same as a inertial frame of reference, is that true?

No. It would be appropriate to say that there are an infinite number of Cartesian coordinate systems that could be applied to an inertial frame of reference. For example. the desk you are sitting at makes a good inertial frame of reference but there is no stricture as to which edge is X, which is Y, and which is Z and even more to the point, there is no stricture that an applied Cartesian system even use the edges for X, Y, and Z.

Further, there is nothing to stop you from applying a Cartesian coordinate system to a non-inertial frame of reference.

 

[physics user1]

No. It would be appropriate to say that there are an infinite number of Cartesian coordinate systems that could be applied to an inertial frame of reference. For example. the desk you are sitting at makes a good inertial frame of reference but there is no stricture as to which edge is X, which is Y, and which is Z and even more to the point, there is no stricture that an applied Cartesian system even use the edges for X, Y, and Z.

Further, there is nothing to stop you from applying a Cartesian coordinate system to a non-inertial frame of reference.

But when we solve a problem we are used to set a frame of reference and a frame of reference has x,y and z axis so isn't it like a cartesian system?

 

[David Lewis]

A Cartesian coordinate system is abstract. An inertial frame of reference is real.

 

[jbriggs444]

But when we solve a problem we are used to set a frame of reference and a frame of reference has x,y and z axis so isn't it like a cartesian system?

You can get through a lot of physics without ever carefully distinguishing between a "frame of reference" and a "coordinate system". If you take a course on linear algebra, the distinction is made clear.

In linear algebra, one has "vectors" in a "vector space". These vectors are not the ordered pairs and ordered triples that you are used to. They are abstract and are only required to adhere to some simple rules about addition and multiplication by "scalars". You can Google for "vector space" to see details. One can attach a coordinate system to a vector space by picking out a particular set of basis vectors (think of them as unit vectors in chosen x, y and z directions) and expressing any vector in the space as a linear combination of those particular x, y and z unit vectors.

That is what Phinds is talking about -- attaching a coordinate system to a particular vector space. The vector space (i.e. the frame of reference) is more general than any particular cartesian coordinate system attached to it.

 

[hackhard]

can a spherical or cylindrical or any other coordinate system be used for a frame of reference to define vectors

 

[physics user1]

You can get through a lot of physics without ever carefully distinguishing between a "frame of reference" and a "coordinate system". If you take a course on linear algebra, the distinction is made clear.

In linear algebra, one has "vectors" in a "vector space". These vectors are not the ordered pairs and ordered triples that you are used to. They are abstract and are only required to adhere to some simple rules about addition and multiplication by "scalars". You can Google for "vector space" to see details. One can attach a coordinate system to a vector space by picking out a particular set of basis vectors (think of them as unit vectors in chosen x, y and z directions) and expressing any vector in the space as a linear combination of those particular x, y and z unit vectors.

That is what Phinds is talking about -- attaching a coordinate system to a particular vector space. The vector space (i.e. the frame of reference) is more general than any particular cartesian coordinate system attached to it.

So... a frame of reference is a "space" where I can stick a coordinate system to describe with a linear combination vectors like forces and displacements. So the coordinate system i stick to the vector space is not the vector space ---> a frame of reference is not the coordinate system right? Thanks to all for the answers, can someone please put an image of the vectors space and of the coordinate system (in the same image) so I can visualize it?

 

[jbriggs444]

So... a frame of reference is a "space" where I can stick a coordinate system to describe with a linear combination vectors like forces and displacements. Thanks to all for the answers, can someone please put an image of the vectors space and of the coordinate system (in the same image) so I can visualize it?

Did you try to figure out what a "vector space" is yet?
How about "linear combination"?
How about "basis"?

 

[jbriggs444]

can a spherical or cylindrical or any other coordinate system be used for a frame of reference to define vectors

Given a liberal reading of the question, the answer is "yes, trivially".

A coordinate system is a way of assigning tuples of coordinate values to points in an underlying space. Let us hand-wave away the annoying problem of points that may have more than one set of coordinate values (for instance, the origin in polar, spherical or cylindrical coordinates). For every point in the space there is a unique coordinate tuple. For every valid coordinate tuple there is a unique point.

If the underlying set of points forms a vector space for some definition of addition and scalar multiplication then so does the set of coordinate tuples under the corresponding definitions of addition of coordinates and multiplication of coordinate tuples by scalars.

But note that the "addition" and "multiplication" operations on coordinate tuples in a non-cartesian coordinate system may not be component-wise addition and multiplication.

 

[hackhard]

a frame of reference is not the coordinate system right?

reference frame = a unique perspective of describing nature
when you say body is accelerating , rotating , translating, has constant momentum , you need to also say from which frame of reference.
coordinate system = ordered tuple of min parameter that can uniquely and completely define every point or vector in space
refrence frame "uses" a coordinate system to describe motion and position of bodies (ie vectors and scalars) as well as other frames
although a reference frame can be uniquely and completely defined by defining its coordinate system at every point of time., both are not exactly the same

 

[hackhard]

from an ant's perspective , a rat is very huge . from humans perspective rat is very small.
since ant compares others to its own size, and human compares others to its own size,
(here " ant's perspective" and "humans perspective" is analogous to reference frame.)
(here "size of ant" is "coordinate system" for "ant's perspective" ie for "ant frame"
here "size of human" is "coordinate system" for "human's perspective" ie for "human frame"

 

[FactChecker]

"Inertial reference" and "cartesian" are addressing two different concepts. An inertial reference frame is one that is not accelerating. So Newton's F=mA can be used. It doesn't matter what coordinate system is used to measure positions in an inertial reference frame; it would still be an inertial reference frame. You can use cartesian coordinates, polar coordinates, or not measure position at all.

Cartesian coordinate systems that are not inertial include: position forward, sideways, and up in your car as you drive around; the rotating Earth-centered coordinates; the coordinate system of a maneuvering airplane where +X=out the nose, +Y=out the right wing, +Z=down through the floor.