# Would a uniform circular motion frame be inertial if ω is constant?

1. Sep 9, 2014

### Ascendant78

I'm wondering if someone is observing a situation from a frame moving in a uniform circular motion, would that frame of reference be considered inertial? I'm unsure because of the centripetal acceleration towards the center.

2. Sep 9, 2014

### mathman

Inertial motion is straight line (no acceleration), Circular motion requires constant non-zero acceration.

3. Sep 9, 2014

### olivermsun

It kind of depends why you're in uniform circular motion.

If you're standing on a planet which is rotating, presumably at a constant rate, then your frame of reference would not be inertial. You could detect funny, non-inertial effects like the precession of a pendulum.

If you're in a space capsule that is in a circular orbit around the earth (or the sun) then you and everything you notice in your reference frame are accelerated together, and you would be in essentially an inertial frame.

4. Sep 9, 2014

### A.T.

No. But if the axes are not rotating, just the origin translates in a circle, then it's not a rotating frame either. You don't have centrifugal or Coriolis forces. Just a uniform inertial force field that changes direction, so it is anti parallel to the centripetal acceleration of the frame.

See the frame fixed to the Earth's center here. The inertial force field is on the right. Not that it is not radial (like the Centrifugal force) but uniform:

From : http://www.vialattea.net/maree/eng/index.htm

Last edited by a moderator: Apr 18, 2017
5. Sep 9, 2014

### Ascendant78

Well thanks for all the information. The question I asked pertained specifically to the notion of an observer watching a frictionless puck as it gets pushed from one side of a turntable (moving at uniform circular motion) to another, but the observer is on the turntable. So, the motion for the observer is the circular motion of the turntable, but I wasn't sure whether or not it would be considered an inertial reference frame due to the centripetal acceleration.

6. Sep 9, 2014

### A.T.

If the observer stands on the turn table. then he is not only moving in circles, but also rotating. So in his frame there are also centrifugal and Coriolis forces on the moving puck. His frame is definitely not inertial.

7. Sep 11, 2014

### Staff: Mentor

It the original question had been whether the frame was locally inertial you would be right. But for the question as asked, the answer is "no", not "it depends":

No, the frame is not inertial. However, if the force holding you in uniform motion is gravity and you're only concerned with what's going on very near to the origin, then you may have a very good approximation to an inertial frame. That's why can treat the inside of the ISS as if it were an inertial frame even though it is uniform circular motion about the earth.

8. Sep 11, 2014

### olivermsun

The original question asks whether the frame of reference would be considered inertial, and to answer that I think you would need to know why the question is being asked, e.g., is one trying to answer a definitional question, or is one trying to "do" physics?

We commonly "do" (classical, non-relativistic) physics in rotating "frames" (i.e., the earth) even though the physics are clearly understood to hold locally rather than extending to infinity (or even to other parts of the earth). The "space capsule" example traditionally limits the observations (and physics) to within the space capsule.

As an aside: the ISS is big enough that the approximation begins to break down, i.e., tidal effects are actually noticeable within the station!

Last edited: Sep 11, 2014
9. Sep 11, 2014

### Staff: Mentor

That's interesting, hadn't heard that - thx. Next time I'll have to choose a smaller example