Why is acceleration independent of reference frames?

In summary, the measurement of acceleration is independent of inertial reference frames because there are two types of acceleration - coordinate acceleration and proper acceleration. While coordinate acceleration may vary with different frames, proper acceleration remains constant and is what is physically felt by an observer. In the classical (non-relativistic) case, the change in velocities is frame independent, but in the relativistic case, it is more complex.
  • #1
randomgamernerd
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I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
And, one more question: When we say that displacement or velocity varies with change in reference(inertial) reference frames, are we talking about variation in magnitude only or both magnitude and direction. I think it should be both magnitude and direction.
 
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  • #2
You can derive this directly from the velocity addition formula. Just differentiate it with respect to time.
 
  • #3
randomgamernerd said:
I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
Hi randomgamernerd, welcome to PF!

In relativity there are two different acceleration concepts and it is important to distinguish between the two of them.

One of them is coordinate acceleration, this seems to be the kind of acceleration you are thinking about. You are correct, length contraction and time dilation make it so that different frames disagree on coordinate acceleration.

The other kind is called proper acceleration. This is the acceleration that you physically feel, the acceleration measured by an accelerometer. This acceleration is invariant, and becomes very important as you transition from SR to GR.
 
  • #4
randomgamernerd said:
I want to know why is the measurement of acceleration independent of inertial reference frames?
I mean if displacement, velocity varies with change of inertial reference frames, acceleration should vary.
And, one more question: When we say that displacement or velocity varies with change in reference(inertial) reference frames, are we talking about variation in magnitude only or both magnitude and direction. I think it should be both magnitude and direction.
I suppose that you mean the classical (non-relativistic) case.
In this case, even though the velocity depends on the frame, the change in velocities is frame independent.
This is so because in the non-relativistic limit the transformations between inertial frames are just adding some constant ( velocity) which cancel out when you take the difference.

The relativistic case is a little more complex, as already mentioned (Dale's post).
 
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Likes Dale
  • #5
My apologies for my answer. For some reason I thought this was in the relativity section. My response was probably overboard for a basic general physics question.
 
  • #6
i forgot to give a reply.
Thanks for your answers...
 

Related to Why is acceleration independent of reference frames?

1. What is acceleration and how is it measured?

Acceleration is the rate of change of an object's velocity over time. It is measured in meters per second squared (m/s^2) or in other units such as feet per second squared (ft/s^2). It can be calculated by dividing the change in velocity by the time interval in which the change occurred.

2. Why is acceleration considered independent of reference frames?

This is because acceleration is a physical quantity that is dependent on the object's motion, rather than the observer's frame of reference. This means that no matter what frame of reference an observer is in, the acceleration of an object will remain the same.

3. How does Newton's second law of motion relate to acceleration and reference frames?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the acceleration of an object will be the same in all reference frames, as long as the net force and mass remain constant.

4. What is an inertial reference frame and how does it relate to acceleration?

An inertial reference frame is a frame of reference in which Newton's laws of motion hold true. In these frames, acceleration is considered to be independent of the observer's perspective, as long as there are no external forces acting on the object.

5. Are there any situations where acceleration is not independent of reference frames?

In some extreme cases, such as when an object is moving at very high speeds or is subject to strong gravitational forces, the effects of relativity may come into play and make acceleration dependent on the frame of reference. However, for most everyday situations, acceleration can be considered independent of reference frames.

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