How inertial frame of reference differs from non-inertial frame?

In summary: Newton's 2nd law only works in inertial frames of reference.In summary, the conversation discusses the concept of inertial frames and how they can be recognized from non-inertial frames. It is mentioned that a non-inertial frame can be converted to an inertial frame by incorporating a fictitious force, but this force cannot be transformed away. It is also noted that in an accelerating frame, an object may appear stationary in a non-inertial reference frame and vice versa. However, in a non-inertial frame, the object will only appear stationary for an instant, whereas in an inertial frame, the object will always appear to have a constant acceleration. The concept of "fictitious force" arises in Newton
  • #1
aditya23456
114
0
We know that we can't say whether we are at rest or uniformly moving if we're in a einstein cage..but if the same medium is accelerating/decelerating can we being inside(and can't see outside) claim abt state of cage..?I ve read that a non-inertial can be converted to inertial by incorporating a fictious force..?? Does this fictious force has any orgin.If yes,where this origin disappears when cage stops accelerating.?If there are 2 bodies inside a cage which is accelerating uniformly,does 1 body see other body in rest..?
 
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  • #2
You can tell if your cage is inertial or not simply by using an accelerometer comoving with the cage. If it reads 0 then the cage is inertial.
 
  • #3
well..I remember a example stating why non-inertial frames can be recognised being inside.When the person inside a cage tosses a coin,if the coin falls back in this hand then he's in inertial frame else if it falls right ahead of him or behind he's in decelerating or accelerating frame..but why does this phenomenon occur,why can't the coin in same way as inertial frame fall back into his hand by consuming the acceleration in the air also while tossed
 
  • #4
If the cage is inertial then the coin won't fall back into his hand, it will continue to move in a straight line at a constant speed. That is Newtons first law.
 
  • #5
That is assuming no external forces. Am I in an "inertial coordinate system" sitting here in front of my computer? If I were to toss a coin in the air, it would come back to my hand!
 
  • #6
Any body inside a inertial frame is a source of non-inertiality because the body is held intact by forces..does that mean there's NO INERTIAL FRAME in known physical applications.?
 
  • #7
HallsofIvy said:
Am I in an "inertial coordinate system" sitting here in front of my computer?
According to GR, no.
HallsofIvy said:
If I were to toss a coin in the air, it would come back to my hand!
Because your frame is non-inertial.
 
  • #8
aditya23456 said:
Any body inside a inertial frame is a source of non-inertiality because the body is held intact by forces..does that mean there's NO INERTIAL FRAME in known physical applications.?
As long as the net real force is zero an object may be subject to multiple external forces and still be inertial. Similarly with the various sub-parts of an extended body.
 
  • #9
Ah. So a room stationary on the surface of the Earth is "non-inertial" and a room falling with non-zero accleration due to gravity is "inertial".
 
  • #10
HallsofIvy said:
Ah. So a room stationary on the surface of the Earth is "non-inertial" and a room falling with non-zero acceleration due to gravity is "inertial".
Yes, although to be precise and avoid ambiguity it would be better to say "non-zero acceleration relative to the Earth's surface". A free-falling room has zero "proper acceleration" i.e. acceleration relative to a local inertial observer.
 
  • #11
HallsofIvy said:
Ah. So a room stationary on the surface of the Earth is "non-inertial" and a room falling with non-zero accleration due to gravity is "inertial".
Yes. In GR gravity is an inertial force which appears only in non-inertial frames. An answer to the OPs question valid for both: Newton and GR is:

Inertial frames are those where all inertial forces disappear (all Newtons Laws hold).

The difference is only the classification of gravity as a interaction or inertial force respectively.
 
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  • #12
The coin trick has to assume that the coin is not charged, or that there is no external electro-magnetic field (or both). Only gravity gets to modify what you call "inertial" or not.
 
  • #13
My question is still not answered completely.! Whats use of fictious force in this context..and how to convert a non-inertial frame to inertial frame.and does a body appear stationary when watched by a object in its accelerating frame.
 
  • #14
aditya23456 said:
My question is still not answered completely.! Whats use of fictious force in this context..and how to convert a non-inertial frame to inertial frame.and does a body appear stationary when watched by a object in its accelerating frame.

You cannot convert a non inertial frame to an inertial frame. The proper force experienced in a non inertial frame cannot be transformed away. We can sometimes use the concept of an "instantaneous co-moving inertial reference frame" to study non inertial frames. For example let us say we have a rocket accelerating with a constant proper acceleration of one g. In an initial reference frame S, the velocity of the rocket is zero. At a later time the rocket is momentarily at rest in inertial reference frame S' which is moving at 0.6c relative to S. At an even later time the rocket is momentarily at rest in an inertial reference frame S'' moving at 0.8c relative to S and so on. In inertial reference frames, S, S' and S'' the rocket is always measured to have an acceleration of g when the rocket is momentarily at rest, but in frame S for example, the initial acceleration is g but progressively the acceleration gets slower as the velocity of the rocket increases relative to S.

Now if we have object accelerating with constant proper acceleration then there exists a non inertial reference frame, in which the object will appear stationary. If we have an inertial object that is accelerating from the point of view of a non inertial reference frame, then there is also exists an inertial reference frame in which the object appears to be stationary. This is trivially obvious. However, if we have a non inertial object experiencing proper acceleration, then there is no inertial reference frame where the object appears stationary for more than an instant. Conversely, if we have a inertial object with coordinate acceleration as measured in a non inertial reference frame, then there is no non inertial reference frame where the object appears stationary for more than an instant.
 
  • #15
The concept of "fictitious force" arises in Newtonian (non-relativistic) physics. For example, relative to a rotating frame of reference, Newton's 2nd law F=ma=dp/dt doesn't work, but we can make it work by adding in a centrifugal "force" and a coriolis "force". Because these forces don't exist in an inertial frame, these forces are usually described as "fictitious forces".

In relativity this is taken account of by the difference between a coordinate derivative and a covariant derivative. Newton's law in a non-inertial frame becomes[tex]
F^\alpha = \frac{\mbox{D} P^\alpha}{\mbox{D} \tau} = \frac{\mbox{d} P^\alpha}{\mbox{d} \tau} + \Gamma^\alpha_{\beta\gamma} U^\beta P^\gamma
[/tex]The term involving [itex]\Gamma^\alpha_{\beta\gamma}[/itex] is the "fictitious force" term and becomes zero in an inertial frame.

In general relativity, gravity becomes a fictitious force. A free-falling inertial observer feels no force of gravity. An observer on the Earth's surface is experiencing a proper acceleration upwards and zero acceleration relative to the Earth. The fictitious weight of the observer makes Newton's Law work relative to the Earth's surface.
 

1. What is an inertial frame of reference?

An inertial frame of reference is a coordinate system in which Newton's first law of motion holds true. This means that an object at rest will remain at rest and an object in motion will continue to move in a straight line at a constant speed, unless acted upon by an external force.

2. How does an inertial frame of reference differ from a non-inertial frame?

In an inertial frame of reference, there are no external forces acting on the objects within the frame, so they will move according to Newton's first law. In a non-inertial frame, there are external forces present, such as gravity or acceleration, which will cause objects to deviate from their expected path.

3. Can you provide an example of an inertial frame of reference?

An example of an inertial frame of reference would be a train moving at a constant speed on a straight track. From the perspective of someone on the train, objects within the train will appear to be at rest or moving at a constant speed. This is because the train is not accelerating and no external forces are acting on it.

4. How is the concept of inertia related to inertial frames of reference?

Inertia is the tendency of an object to resist changes in its state of motion. In an inertial frame of reference, objects will continue to move at a constant speed due to their own inertia, unless acted upon by an external force. This is why Newton's first law is also known as the law of inertia.

5. What are some practical applications of understanding inertial frames of reference?

Understanding inertial frames of reference is important in many fields, such as physics, engineering, and navigation. For example, it is crucial in designing and operating spacecraft and satellites, which operate in the absence of external forces. It also allows for accurate measurements and predictions of motion in various systems.

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