How do you tell you are not in inertial frame of reference

In summary, the conversation discusses inertial and non-inertial frames of reference, using the example of two people in a rotating disk. It is argued that the person inside the disk can determine if they are in an inertial frame by observing the motion of objects around them, as in an inertial frame F=ma. This leads to a discussion of freefall and the concept of an inertial frame in the context of gravity. The conversation also touches on the ideas of fictional forces and Newton's laws.
  • #1
the-genius
24
0
While explaining about inertial and non-inertial frame of reference, people give this example--
http://www.phys.unsw.edu.au/einsteinlight/jw/module1_Inertial.htm
if you don't wish to follow the link, here is a simple explanation--->
there are two person and a rotating disk. Person A is in rotating disk and person B outside.
Both will see each other revolving around. But when person A throws a ball towards the rotating person B it won't straight but curving round to meet Person B, but however If person B throws a ball then it goes straight.

I think the flaw here is asuming that the force that provides centripetal force to the Person A,(may be frictional force here), is applied to the Person only but not the ball. What if the ball was rolled out on the disk and it had les assume: infinite friction (so that, when the ball is just placed on the side of person A, it won't shoot out of the disk, due to the same friction that holds person A), then the ball will go straight for person A, But curving for person B. Now, can you say Person A is in inertial Frame of reference.
 
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  • #2
the-genius said:
While explaining about inertial and non-inertial frame of reference, people give this example--
http://www.phys.unsw.edu.au/einsteinlight/jw/module1_Inertial.htm
if you don't wish to follow the link, here is a simple explanation--->
there are two person and a rotating disk. Person A is in rotating disk and person B outside.
Both will see each other revolving around. But when person A throws a ball towards the rotating person B it won't straight but curving round to meet Person B, but however If person B throws a ball then it goes straight.

I think the flaw here is asuming that the force that provides centripetal force to the Person A,(may be frictional force here), is applied to the Person only but not the ball. What if the ball was rolled out on the disk and it had les assume: infinite friction (so that, when the ball is just placed on the side of person A, it won't shoot out of the disk, due to the same friction that holds person A), then the ball will go straight for person A, But curving for person B. Now, can you say Person A is in inertial Frame of reference.
Nope, because the friction is a force acting on the ball, then. If the frame were inertial, the ball would travel in a straight line with no force acting on it. Because F=ma in an inertial frame. And in your example, the acceleration of the ball observed by the inertial observer (outside the disk) would be proportional to the frictional force acting on the ball. Again because F=ma in an inertial frame.

An inertial frame is identified by the fact that F=ma, that's why the ball will travel in a straight line as observed from an inertial frame, if there is no force acting on it.
 
  • #3
How does person A knows (by mere looking) that the ball is going straight due to frictional force but not because Its in inertial frame. I think he will be free to say anything.
 
  • #4
the-genius said:
How does person A knows (by mere looking) that the ball is going straight due to frictional force but not because Its in inertial frame. I think he will be free to say anything.
Well, he might have to make other observations to determine he is not at rest in an inertial frame, if he can't verify that the ball has a force acting on it. But notice how easy that would be. There will be "fictional" forces acting on everything that is not tied down, including any celestial object he observes.

It's important to note that the very definition of an inertial frame is one in which F=ma and there are no "fictional" forces acting on any objects.
 
  • #5
I am asking the very question, what experiment would he carry out to test whether he is in inertial frame or not.. (but remember that if he is provided a fictional force so should every objects he will experiment with.)
 
  • #6
the-genius said:
I am asking the very question, what experiment would he carry out to test whether he is in inertial frame or not.. (but remember that if he is provided a fictional force so should every objects he will experiment with.)
He could release a ball into freefall and see if F=ma (ball travels in straight line when it's not in contact with anything).

Or he could notice that person B is going around him in circles.

Or he could measure the force acting on an object attached to the disk indirectly with a spring.

There are many specific ways to tell, but they are all based on the fact that F=ma in an inertial frame. Any experiment that can measure force applied and relative velocity of an object will work. Of course it's easier to just release an object into freefall with zero applied force and measure its velocity over time.

In an inertial frame, an object in freefall will travel in a straight line with constant speed.
 
  • #7
In a noninertial frame, you can ascribe accelerations to forces (from material bodies), but not all forces will be in a third law pair, ie. the second law will work, but the third law will not.
 
  • #8
Al68, if you are in a box free-falling (acclerating with g) on earth, would you consider this box, a inertial frame of refernce?
If no, then why not? If you leave a ball ball here, it will obey F=ma (at leat for you). If you throw it, it will move in constant line with respect to you, following Newtons law. How, then it can't be inertial frame of reference?
 
  • #9
the-genius said:
Al68, if you are in a box free-falling (acclerating with g) on earth, would you consider this box, a inertial frame of refernce?

Yes, in the limit of a small enough box that tidal effects are not noticeable. This line of thought led Einstein to General Relativity, in which gravitation is not a force.
 
  • #10
the-genius said:
Al68, if you are in a box free-falling (acclerating with g) on earth, would you consider this box, a inertial frame of refernce?
If no, then why not? If you leave a ball ball here, it will obey F=ma (at leat for you). If you throw it, it will move in constant line with respect to you, following Newtons law. How, then it can't be inertial frame of reference?
Yes, the box would be an inertial reference frame (approximately, disregarding tidal effects like jtbell pointed out).

An observer stationary on Earth's surface is non-inertial, with a 1 G proper acceleration. That's why we feel the force of the ground pushing up against our feet just like we would in a ship in deep space accelerating at 1 G. And the relative acceleration of objects in freefall further shows that Earth's surface is not an inertial frame.

That's how modern physics treats it. Classical physics treated an observer on Earth's surface as (approximately) inertial, and gravity as an applied force. In which case, the F in F=ma was attributed to the "force" of gravity, and accounted for a freefalling objects relative acceleration. For our purposes in this thread, we could use either modern or classical physics and the results would be the same.
 
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  • #11
the-genius said:
I am asking the very question, what experiment would he carry out to test whether he is in inertial frame or not.
He can read an accelerometer. If it reads 0 then it is inertial, otherwise it is non-inertial.
 
  • #12
One thing that may be helpful is to distinguish between local and global inertial frames. In special relativity, global Lorentz inertial frames exist. The Rindler frame of a constantly accelerated observer is not a global Lorentz inertial frame, but there are local Lorentz inertial frames almost everywhere in the Rindler frame. "Inertial frame" usually means "global inertial frame".
 
  • #13
How do you distinguish global and local inertial frames, atyy, please please explain in your own words (I wouldn't like a link to a lengthy explanation with difficult maths, I just need the concept)
 
  • #14
A global inertial frame is one where any accelerometer at rest anywhere will read 0.
 
  • #15
What DaleSpam said (twice).

I'm just going to add that the motion of an accelerometer that reads zero doesn't define an inertial frame by itself. It defines the time axis. You need to have a clock moving with the accelerometer in order to assign coordinates to events on the time axis, and then you have to use the usual synchronization procedure to assign coordinates to events that aren't on the time axis. The basic idea is that if light is emitted in the positive x direction at (-T,0), then reflected somewhere, and finally detected at (T,0), the coordinates of the reflection event are (0,cT).
 
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  • #16
Fredrik said:
I'm just going to add that the motion of an accelerometer that reads zero doesn't define an inertial frame by itself.
Good point. It only defines an inertial observer. Thanks for the clarification about how to extend that to an inertial frame.
 
  • #17
Emphasis mine ...
Fredrik said:
I'm just going to add that the motion of an accelerometer that reads zero doesn't define an inertial frame by itself. It defines the time axis. You need to have a clock moving with the accelerometer in order to assign coordinates to events on the time axis, ...
An accelerometer located at the center of mass of a free-falling spacecraft (which is the ideal location for an accelerometer) will measure zero whether or not the spacecraft is rotating. Just because the accelerometer reads zero does not mean the frame is inertial. It means the accelerometer is free-falling, and nothing else.

A reference frame comprises an origin and a set of axes. To determine whether a reference frame is inertial you also need to know whether the frame is rotating. Fortunately, instruments exist (e.g., rate-based gyros) to do just that.
 
  • #18
I'd like to point out that it's Newton's third law that brings consistency to our ability to detect whether we're in an inertial reference frame.

If you wonder whether you're in an inertial reference frame, and you witness an accelerating object, then you need a way -- at least in principle -- to tell whether the object is accelerating because of a real force or because of a "fictitious force."

If it's a real force, then the third law requires there to be some other object out there that's experiencing the equal and opposite force.
 
  • #19
DH posted:
To determine whether a reference frame is inertial you also need to know whether the frame is rotating. Fortunately, instruments exist (e.g., rate-based gyros) to do just that.

Hey fantastic...I knew rate based gyros do a superior job as steering instruments aboard boats in rough seas...but I did not know that the "rate" was measuring accleration...My own automatic steering is controlled by a traditional gyro compass (no rate feature) and often I can do a better job manually by anticipating approaching waves...but its tiring...
 
  • #20
Naty1 said:
Hey fantastic...I knew rate based gyros do a superior job as steering instruments aboard boats in rough seas...but I did not know that the "rate" was measuring accleration...My own automatic steering is controlled by a traditional gyro compass (no rate feature) and often I can do a better job manually by anticipating approaching waves...but its tiring...
It's not. Rate-based gyros measure angular velocity, not acceleration.
 
  • #21
What you all are missing is I think, globalization of inertial frame. How can we consider (according to your theories) Earth as inertial frame as it is in constant (centripetal) acceleration due to rotation around the sun. What i mean to say is, inertial frame are not global they are relative. We can Say, A is an inertial frame with respect to B. But Both A & B may not be inertial frame with respect to a third co-ordinate system (accelerating relative to A&B) say: C.
Am I wrong?
 
  • #22
Yes, you are wrong. Whether or not an observer is inertial is frame invariant. "Inertialness" is not relative. If A is inertial then its relationship to B or C is irrelevant.
 
  • #23
Cantab Morgan said:
I'd like to point out that it's Newton's third law that brings consistency to our ability to detect whether we're in an inertial reference frame.
This thread is in the Special & General Relativity section, so answers should be couched in terms of inertial frames in GR. A reference frame with non-rotating axes and origin at the center of a spacecraft subject only to gravitation is an inertial frame in GR but not in Newtonian mechanics.

Moreover, this answer is wrong even in the context of Newtonian mechanics. Newton's laws are only valid in an inertial frame. Newton's 1st law essentially defines an inertial frame. If an observer sees an accelerating object that is known to have no forces acting on it, the observer's reference frame is not inertial -- in the context of Newtonian mechanics.

the-genius said:
What you all are missing is I think, globalization of inertial frame. How can we consider (according to your theories) Earth as inertial frame as it is in constant (centripetal) acceleration due to rotation around the sun. What i mean to say is, inertial frame are not global they are relative. We can Say, A is an inertial frame with respect to B. But Both A & B may not be inertial frame with respect to a third co-ordinate system (accelerating relative to A&B) say: C.
Am I wrong?
Yes, you are wrong, and in both Newtonian mechanics and GR. In Newtonian mechanics, inertial frames have global extent and all inertial frames are related to on another by having zero relative rotation and zero relative acceleration. In GR, inertial frames have local extent only. A non-rotating Cartesian frame with origin at the center of the Earth is not an inertial frame far from the center of the Earth. Falling apples accelerate and hit observers on the head in such a frame.

On the other hand, rotation is global in GR as far as I know. Somebody throw an apple at me if I'm wrong; preferably not a rotten apple.
 
  • #24
D H said:
Moreover, this answer is wrong even in the context of Newtonian mechanics. Newton's laws are only valid in an inertial frame. Newton's 1st law essentially defines an inertial frame. If an observer sees an accelerating object that is known to have no forces acting on it, the observer's reference frame is not inertial -- in the context of Newtonian mechanics.

Apparently I failed to express my point clearly. How can you tell that the accelerating object is known to have no forces acting on it? Newton's third law. If there's no other object being acted upon by an equal and opposite force, then the force must be fictitious.
 
  • #25
Newton's third law is not a good test because it is not universally true, even in classical mechanics. The lack of acceleration given the lack of any force, period, is a good test of an inertial frame -- in the realm of Newtonian mechanics, that is. This thread is not about inertial frames in Newtonian mechanics. It is about inertial frames in the context of special and general relativity.
 
  • #26
D H said:
This thread is not about inertial frames in Newtonian mechanics. It is about inertial frames in the context of special and general relativity.

This point is especially well taken, and I shall therefore disengage.
 
  • #27
the-genius said:
How do you distinguish global and local inertial frames, atyy, please please explain in your own words (I wouldn't like a link to a lengthy explanation with difficult maths, I just need the concept)

A global inertial frame is one in which the "laws of physics" have their "standard form" everywhere. In classical special relativity, the "laws of physics" would be Maxwell's equations and the special relativistic version of the Lorentz force law; in quantum field theory, they would be the standard model of particle physics. A common way of defining "standard form" is that the representation of the metric tensor in the "laws of physics" should be diagonal with elements (-1,1,1,1). In a local inertial frame, the metric has that exact form only at the origin.
 

1. How do you determine if you are in an inertial frame of reference?

To determine if you are in an inertial frame of reference, you can perform a simple thought experiment known as the "free-fall test". If you are in a frame of reference that is not accelerating, objects will appear to fall straight down when dropped. However, if you are in a non-inertial frame of reference, objects will appear to fall at an angle due to the acceleration of the frame.

2. What is the difference between an inertial and a non-inertial frame of reference?

An inertial frame of reference is a frame in which Newton's first law of motion holds true. This means that an object will remain at rest or in motion with constant velocity unless acted upon by an external force. In contrast, a non-inertial frame of reference is one that is accelerating, causing objects to appear to move differently than they would in an inertial frame.

3. Can you feel or sense if you are in a non-inertial frame of reference?

No, you cannot feel or sense if you are in a non-inertial frame of reference. This is because the laws of physics are the same in all inertial frames of reference, so there is no physical way to determine if you are in a non-inertial frame without performing a test or experiment.

4. What types of motions can cause a frame of reference to be non-inertial?

A frame of reference can be non-inertial due to various types of motion, such as rotation, circular motion, and linear acceleration. For example, if you are on a spinning amusement park ride, your frame of reference will be non-inertial due to the circular motion.

5. Why is it important to know if you are in a non-inertial frame of reference?

It is important to know if you are in a non-inertial frame of reference because the laws of physics behave differently in these frames. This can have implications in various fields, such as astrophysics and engineering, where precise measurements and calculations are necessary. Additionally, understanding inertial frames of reference is essential for comprehending the fundamental principles of motion and the universe.

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