Non inertial or inertial reference frame?


by Lengalicious
Tags: frame, inertial, reference
Lengalicious
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#1
Apr25-12, 10:40 AM
P: 146
1. The problem statement, all variables and given/known data
Specify and explain whether the following is an inertial or non-inertial observer: An observer is placed on a rock between Andromeda and the Milky Way.


2. Relevant equations

N/a

3. The attempt at a solution
So here is my understanding, the observer would be situated within an inertial reference frame as it is not specified whether there is an acceleration relative to either of the galaxies, my curiosity is that since the Andromeda galaxy is traveling towards the Milky Way does this mean that the observer is in fact accelerating relative to Andromeda? Or is the observer still stationary relative to Andromeda? Bit confused, I'd be more than grateful for any clarification.
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gneill
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#2
Apr25-12, 11:40 AM
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The observer is in free-fall. Suppose he was enclosed in a sealed lab and could conduct any experiments he wished entirely within that lab (no reference to anything outside the lab). Can you think of any experiment he might perform that would determine whether or not his lab frame of reference is inertial or not?
Lengalicious
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#3
Apr25-12, 11:44 AM
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Erm maybe place a ball somewhere in the lab and see whether it moves or not?

gneill
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#4
Apr25-12, 11:47 AM
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Non inertial or inertial reference frame?


Quote Quote by Lengalicious View Post
Erm maybe place a ball somewhere in the lab and see whether it moves or not?
And what would happen?
Lengalicious
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#5
Apr25-12, 11:48 AM
P: 146
Well if the lab was in an inertial frame then the ball would stay put, if it was non inertial then the ball would move in the opposite direction to the net force on the lab no?
gneill
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#6
Apr25-12, 11:50 AM
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Quote Quote by Lengalicious View Post
Well if the lab was in an inertial frame then the ball would stay put, if it was non inertial then the ball would move in the opposite direction to the net force on the lab no?
True. But what do you say will happen to the ball in this particular case? Will the ball stay put or not?
Lengalicious
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#7
Apr25-12, 11:52 AM
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Quote Quote by gneill View Post
True. But what do you say will happen to the ball in this particular case? Will the ball stay put or not?
Sorry, i think i've misunderstood the 'case'. Not sure how you can specify what happens to the ball if the frame of reference is unknown? I guess it just stays put because its frame is not relative to anything? Its a similar case as a particle in space with no other particles in existence right? the particle does not move because there is no relativity.
gneill
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#8
Apr25-12, 12:00 PM
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Quote Quote by Lengalicious View Post
Sorry, i think i've misunderstood the 'case'. Not sure how you can specify what happens to the ball if the frame of reference is unknown? I guess it just stays put because its frame is not relative to anything?
The idea is to use what you know about the situation to deduce whether or not the frame of reference can be considered to be an inertial one. For the ball to move with respect to the lab there would have to be some motion that ball partakes in that is different from the motion that the lab itself pursues. In this case you know that the lab is in free-fall in whatever small and locally uniform gravitational field that exists this far away from any large bodies.

How do bodies of different mass 'fall' in a uniform gravitational field?
Lengalicious
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#9
Apr25-12, 12:07 PM
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Quote Quote by gneill View Post
The idea is to use what you know about the situation to deduce whether or not the frame of reference can be considered to be an inertial one. For the ball to move with respect to the lab there would have to be some motion that ball partakes in that is different from the motion that the lab itself pursues. In this case you know that the lab is in free-fall in whatever small and locally uniform gravitational field that exists this far away from any large bodies.

How do bodies of different mass 'fall' in a uniform gravitational field?
They would accelerate in the field relative to whatever mass is creating the field, so they would be within a non-inertial reference frame? I'm still not sure of the answer to my initial question, an observer is stationed on a rock between 2 galaxies. This is all the information i'm given. I imagine the galaxies are both having a gravitational effect on the rock? So does it accelerate towards one of the galaxies?
gneill
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#10
Apr25-12, 12:18 PM
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Quote Quote by Lengalicious View Post
They would accelerate in the field relative to whatever mass is creating the field, so they would be within a non-inertial reference frame? I'm still not sure of the answer to my initial question, an observer is stationed on a rock between 2 galaxies. This is all the information i'm given. I imagine the galaxies are both having a gravitational effect on the rock? So does it accelerate towards one of the galaxies?
While it may be true that the laboratory is accelerating with respect to the galaxies as it falls in the net gravitational field, the laboratory is hermetically sealed and the observer cannot perform any observations of anything outside the lab (no windows, no doors, no cameras mounted outside, no contact with outside).

Inside the lab, will the ball move with respect to the lab? Do things fall at different rates and/or directions in a uniform gravitational field?
Lengalicious
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#11
Apr25-12, 12:28 PM
P: 146
Oh right, yeh think i get what you were getting at now, yeh the ball WILL move with respect to the lab in the field. Still not sure how i relate this to my question though, so do i treat the rock as the lab and the observer as the ball... The observer moves relative to the rock? But then how do i know if hes inertial or not?
gneill
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#12
Apr25-12, 12:37 PM
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Quote Quote by Lengalicious View Post
Oh right, yeh think i get what you were getting at now, yeh the ball WILL move with respect to the lab in the field. Still not sure how i relate this to my question though, so do i treat the rock as the lab and the observer as the ball... The observer moves relative to the rock? But then how do i know if hes inertial or not?
Why would the ball move with respect to the lab? The lab is not being held stationary in space is it? I thought it was sitting on a rock that's in free-fall; just 'floating' in space.
Lengalicious
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#13
Apr25-12, 12:47 PM
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Quote Quote by gneill View Post
Why would the ball move with respect to the lab? The lab is not being held stationary in space is it? I thought it was sitting on a rock that's in free-fall; just 'floating' in space.
Ok, i think the lab analogy has confused me a bit, so basically the lab is stationary in space, not accelerating relative to anything therefore the ball in the lab cant be moving with respect to the lab since the ball is just sitting there as there are no net forces on the ball? So the frame of reference of the ball is inertial?
EmittingLight
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#14
Apr25-12, 12:52 PM
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Erm I just thought I'd clarify what the definition of an inertial reference frame is, since the OP has used terms/reasoning which implies that they haven't got a strong grasp on it. From the Wikipedia article:
"An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed."

I italicised the part I felt was important (i.e. things can accelerate according to an inertial frame, but only if a force is acting on it). Also, think of the 'frame of reference' as being a pair of eyes; they have to see the particle (that is not acted on by a force) move in a straight line.
gneill
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#15
Apr25-12, 01:14 PM
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Quote Quote by Lengalicious View Post
Ok, i think the lab analogy has confused me a bit, so basically the lab is stationary in space, not accelerating relative to anything therefore the ball in the lab cant be moving with respect to the lab since the ball is just sitting there as there are no net forces on the ball? So the frame of reference of the ball is inertial?
Okay, the first thing to grasp is that there is no such thing as 'stationary in space'. This is not because nothing can 'hold still', but because there is no absolute frame of reference that we can call 'space'. That is, there is no preferred frame of reference to which we can assign the designation "absolutely no motion", or "absolute rest". All frames are relative.

In your proposed experiment the ball will NOT move with respect to the lab. Both the lab and the ball will move IDENTICALLY in any uniform background gravitational field. Remember Galileo's dropping of objects of different mass? They took the same time to fall, right?

The point is, the present experiment will not detect that your 'guy on a rock' comprises a non-inertial frame of reference. And in fact, there is NO experiment that an observer in such a situation can do that would distinguish his frame of reference from an inertial frame of reference whether he uses masses, sound, light, chemistry, or anything else. So if the frame of reference is indistinguishable from an inertial frame, what must you conclude?

For future reference, any free-falling body in space follows a path that is called an inertial trajectory
EmittingLight
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#16
Apr25-12, 01:46 PM
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I don't think that a frame being accelerated by gravity constitutes an inertial reference frame, and I also think that this means that there can not possibly be an inertial frame in our universe, at least not according to classical physics (i.e. gravitational force acts instantaneously regardless of distance).

Just because the ball remains at rest relative to the lab frame, it doesn't mean that the lab is inertial; the ball is only at rest relative to the lab because it has a force (from gravity) acting on it such that it maintains at rest, but if you were to remove that gravitational force (and hence have it undergo true inertial movement), it will no longer be stationary according to the lab frame anymore (because the lab is being accelerated by the gravity).
gneill
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#17
Apr25-12, 02:00 PM
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Quote Quote by EmittingLight View Post
I don't think that a frame being accelerated by gravity constitutes an inertial reference frame, and I also think that this means that there can not possibly be an inertial frame in our universe, at least not according to classical physics (i.e. gravitational force acts instantaneously regardless of distance).

Just because the ball remains at rest relative to the lab frame, it doesn't mean that the lab is inertial; the ball is only at rest relative to the lab because it has a force (from gravity) acting on it such that it maintains at rest, but if you were to remove that gravitational force (and hence have it undergo true inertial movement), it will no longer be stationary according to the lab frame anymore (because the lab is being accelerated by the gravity).
If you remove the gravitational force then the ball and lab will still be experiencing the same relative motions. The gravitational force, whether zero value or nonzero value, as long as it's the same, encompasses all of the lab including the lab itself. You cannot switch off gravity in only one part of the lab (if you can, you'll be headed to Stockholm shortly!).

There is NO experiment that you can do within the lab that can detect the lab's motion. All laws of physics behave there as though they take place in an inertial frame of reference.

A body in free-fall comprises an inertial frame of reference.
EmittingLight
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#18
Apr25-12, 02:29 PM
P: 17
The point isn't about what we can and can't do though; the ball has a force acting on it, so it no longer has to have a straight line trajectory according to an inertial reference frame, in fact I think it can not possibly have a straight line trajectory (it only has one in a non-inertial reference frame with the same acceleration).

Think of the lab as a spaceship at some hypothetical place with zero gravity, and the ball as a much smaller spaceship inside the lab. You're saying that if they both fire their rockets to have the same acceleration (i.e. they are both accelerated by the same gravitational force), hence their motions would be indistinguishable, that they both constitute inertial reference frames.

Now let's say we attach a straight, easily tilted, rod to both of the spaceships, and have one of the spaceships turn off their rocket. Both spaceships will be accelerating according to each other, but only one of them will have a rod that's not tilted: this is the one with the rockets turned off, and the one that is considered the inertial reference frame.

EDIT: I have to go to sleep now, and when I wake up I'll be busy, so it will be many hours before I can continue this discussion.


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