# How a rotational motion could be in an inertial ref. frame

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1. Dec 22, 2015

### albertov123

When rotation exists, so does the radial acceleration. It can be defined as ar=-ω2xr

So there is a kind of acceleration with rotation all the time. Thus, we have to use non-inertial reference frame all the time.

Could a rotational movement be analysed in an inertial ref. frame?

2. Dec 22, 2015

### A.T.

You are confusing the motion of the physical bodies with the motion of the reference frame.

3. Dec 22, 2015

### albertov123

Oh, you are saying that a rotational motion could be considered in an inertial ref. frame.

Then, let me dive into my source of confusion. We are learning reference frames and when I see a rectilinear acceleration, I understand there is a non-inertial reference frame also accelerating with the physical body. But I'm not clear on when to use inertial or non-inertial in the rotational cases.

Can you give me an example?

4. Dec 22, 2015

### A.T.

For practice, you should analyse it from both reference frames to learn the difference. This will help you to pick the most convenient one later on.

5. Dec 22, 2015

### FactChecker

The first thing to consider about a rotating reference frame is that the second derivative of position is no longer the same as acceleration due to a force. In an inertial reference frame they are the same but not in a rotating reference frame. Suppose you are traveling North in a car at 50 mph, but want to use a rotating reference frame to measure velocities and acceleration. Suppose the rotating frame does a full rotation in 4 minutes. Initially you measure the velocity in one axis as 50 mph. One minute later, you measure the velocity in the other axis as 50 mph and the first axis has gone to 0 mph. So there are large velocity derivatives in the rotating frame. All with no force applied. In the rotating reference frame, you must account for the rotation to convert derivatives to true accelerations due to forces. And the difference between the two can easily be large.

6. Dec 22, 2015

### A.T.

More generally: In non-inertial frames the second derivative of position (coordinate acceleration) times mass is not always equal to the sum of interaction forces (those which obey Newtons 3rd Law). One way of dealing with this, is to introduce inertial forces (which don't obey Newtons 3rd Law), to make at least Newton's 2nd Law work.