Spinning Frame of Reference: Inertial or Non-Inertial?

[alpha372]

Homework Statement

Is a spinning frame of reference an inertial frame of reference?

Homework Equations

net torque, net force = ma, equilibrium --> net force = 0, net torque = 0
I've learned that an inertial frame of reference is a frame of reference which is not accelerating.

The Attempt at a Solution

I would guess that it is, based on the concepts of netwon's first and second law, and equilibrium. If an object is in equilibrium, this means there are no net forces or net torques acting on it. Assuming the spinning "frame of reference" is in equilibrium, then there are no net forces acting on it. No net forces acting on it means that it is not accelerating (f = ma). Since it is not accelerating, it is an "inertial frame of reference". So I believe a frame of reference that is spinning would be an "inertial frame of reference" (assuming the force that caused the torque intially is no longer active). But, I am not confident of my conclusion.

 

[D H]

From the perspective of a rotating reference frame, does a particle that is not subject to any forces obey Newton's first law?

 

[alpha372]

From the perspective of a rotating reference frame, does a particle that is not subject to any forces obey Newton's first law?

Honestly, I am tempted to say that the particle does obey Newton's first law, only because if I think of the Earth spinning, I believe that there are objects within it that obey Newton's first law...although I believe I've run across some text some where that says we're supposed to ignore the fact that the Earth is rotating.

So forget the Earth example. Let's look at a spinning top. A single fragment/ particle of the spinning top would be accelerating because it's center of mass is accelerating... I think I know where you might be trying to lead me...

If the spinning top is made of a bunch of particles that are accelerating, then the spinning top as a whole should be accelerating, but that's not true, the spinning top as a whole is not accelerating-- it is in equilibrium. So if the frame of reference is made of a whole bunch of particles that are accelerating individually, yet together, it must still be in equilibrium too--just like the spinning top. And equilibrium implies no net force, which implies no net acceleration, which to me still implies an inertial frame of reference.

So I'm stuck.

But if we are only considering a single particle in a rotating frame... this is difficult for me to imagine. Jumping back to the Earth example. When we are on the ground, we spin with the earth. It seems like you could say that we are accelerating, since we are traveling in a circle along with the earth. So even if no net force were acting on us, we would be accelerating because of the rotation of the earth, making Newton's first law invalid, seemingly leading to the conclusion that the frame of reference is not an inertial frame of reference.

However, put ourselves at the center of the earth; we would become part of its center of mass; which is not accelerating, just spinning, hence Newton's first law is obeyed, seemingly leading to the conclusion that the frame of reference is an inertial frame of reference.

So this brings about the question I should really be asking: What exactly constitutes a frame of reference?

When I think of a frame of reference, I literally picture a frame that I am looking through. And when I see a spinning frame of reference, I see a picture frame spinning; solid or hollow.

So I'm am at the same place I am before; Is a spinning frame of reference an inertial frame of reference? Now my guess is no. But who cares, I'd like some proof and validation.