Confused about reference frames

[Lengalicious]

Ok I'm really trying to understand inertial and non-inertial reference frames, my understanding is as follows:
A rest observer on the earth, the observer will be stationary relative to the earth.. Now as I understand it an inertial reference frame is one of which 2 coordinate systems are both inertial relative to each other? This means that the observer would be inertial right? Because the observer is stationary (inertial) relative to the Earth and visa versa? I wasn't sure how to take the Earth's rotation into account because I'm not talking about the observer relative the sun or any other celestial object, therefore confined to the reference frame of the observer and earth, any rotation is completely unaccounted for right? As if the Earth wasn't rotating? Now another example is an observer on a merry-go-round. Would this be the same principle or not? Because the observer would be stationary relative to the merry go round and visa versa once again? So the observer would be inertial? Now for a non-inertial example, if the observer is on the ground at rest next to the merry go round, the observer is now accelerating relative to the merry go round and the merry-go-round accelerating relative to the observer right? So the observer is now in a non-inertial reference frame? Have I got this correct or is something misinterpreted? It just seems too obvious to me but I know these frames of reference can be quite complicated? Confused.

 

[chrisbaird]

No. A reference frame that is stationary relative to the Earth's ground is non-inertial because the Earth is rotating. The rotation of the Earth has nothing to do with the sun or stars. It is rotating about its own axis. An inertial frame is more than a frame that is stationary relative to something. Every frame is stationary relative to itself. An inertial frame is one that is not-accelerating as viewed from all other inertial frames. The non-inertial nature of the Earth frame has real effects, such as the Coriolis force, that must be accounted for to get global wind patterns right.

 

[Lengalicious]

Ok so in the case of the observer stationary on the Earth's surface both reference frames are non-inertial relative to one another because the Earth's rotating and therefore the coordinate system of the observer on the Earth must also be rotating? Or is this statement incorrect? And in the case where an observer is next to a spinning merry go round, the observer is in a non-inertial frame relative both to the Earth's surface AND the merry go round? In the case of an observer stationary and a car with constant velocity passing by, the frame of reference is inertial from both points of view yes?

 

[phinds]

Ok so in the case of the observer stationary on the Earth's surface both reference frames are non-inertial relative to one another because the Earth's rotating and therefore the coordinate system of the observer on the Earth must also be rotating? Or is this statement incorrect? And in the case where an observer is next to a spinning merry go round, the observer is in a non-inertial frame relative both to the Earth's surface AND the merry go round? In the case of an observer stationary and a car with constant velocity passing by, the frame of reference is inertial from both points of view yes?

I'm not all too clear on this stuff myself, but I think your continued statements about frames of reference "relative to each other" are confusing you. A frame of reference is not inertial or non-inertial relative to another frame of reference, it is inertial or not based on whether or not it is accelerating. Measurements in all inertial FOR's can be converted to measurements in any other inertial FOR. It's when you start accelerating that all hell breaks loose and things don't match up.

 

[chrisbaird]

Ok so in the case of the observer stationary on the Earth's surface both reference frames are non-inertial relative to one another because the Earth's rotating and therefore the coordinate system of the observer on the Earth must also be rotating? Or is this statement incorrect? And in the case where an observer is next to a spinning merry go round, the observer is in a non-inertial frame relative both to the Earth's surface AND the merry go round? In the case of an observer stationary and a car with constant velocity passing by, the frame of reference is inertial from both points of view yes?

If I am standing motionless on the surface of the earth, then my frame IS the Earth's frame (as long as we choose the same origin). The act of standing on the Earth and my feet being motionless compared to the ground means that I am rotating at the same speed as the earth. We are both therefore in the same non-inertial frame. If I am on the merry-go-round, sitting motionless relative to the horse going round and round, then I am in the merry-go-round's non-inertial frame. As soon as I step off the merry-go-round and my feet are motionless on the ground, I am now in an inertial frame (if you neglect Earth's rotation in this one example).

In reality, perfectly non-inertial frames are hard to come by: The Earth is rotating about its axis. Its also revolving around the sun. Our solar system is also revolving around the center of the galaxy. But for most measurements, these effects are negligible.

Think of it this way. If you are in an inertial frame, there is no preferred frame or origin. There is no way of telling (no experiment you can do to see) if it is you really moving or the other frame really moving. But if you are in a non-inertial frame (spinning or linearly accelerating), the very act of accelerating creates a preferred frame. The man on the merry-go-round gets sick to his stomach, but the man on the ground does not. If you close your eyes in a non-inertial frame, you can "feel" where the absolute coordinate origin of your non-inertial frame is. For example, if you are in a car and it takes a sharp turn, you can tell which way it turned and how fast even with your eyes closed. You could even indicated roughly where the center of its rotational motion is. This is nothing special about space, it is something special about the act of accelerating. On the other hand, in an inertial frame, you can't sense the absolute coordinate origin because there isn't any.