Non-inertial Frame Of Reference

Coriolis forces in a hurricane

I recently did a post on Inertial Frames of Reference (IFoR) so I thought I best complete the picture by doing a post on Non-inertial frames of reference. As we saw in the other post the IFoR turned out to be very similar to my garage. The Non IFoR or NIFoR for short is not like my garage.

Technically a  non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame, a bit like a car decelerating when it is pulling into say, a garage.

So a garage is an inertial reference frame and a car accelerating out of a garage or slowing as it enters the garage is a non-inertial reference frame. Yes, but this doesn't really help, because you would have to be a lunatic to be performing scientific experiments in a car while driving. That said, it is a non-inertial reference frame.

The odd thing is that things get really complicated when you introduce accelerations. The laws of motion in non-inertial frames get more complex and vary from frame to frame depending on the acceleration. Not only that but you have to start inventing forces to account for the observed motion. These include the centrifugal force and the Coriolis force.

Now many people have heard of the centrifugal force, it is the thing that tries to throw you out of the ride at the fair. You feel it, it must exist. Firstly, the centrifugal force is generally confused with the centripetal force. The centripetal force, in the case of something like the earth rotating round the sun, being the force towards the centre of the earth.

The centrifugal force is sometimes called an inertial force or a fictitious force, but this is a "technical" term and all it means is that it disappears when you are stationary, for example, you are in a car going in a straight line at a constant speed, no centrifugal force, you go round a corner all of a sudden we are feeling a force. 

Coriolis Force

Another force is the Coriolis force or Coriolis effect, named after Gaspard Gustave Coriolis who lived in the first half of the 19th century. One cause, or example of the Coriolis effect is that caused by the rotation of the earth and the inertia of the a mass experiencing this rotation. The force is proportional to the mass and the rotation rate. Larger the mass and the speed of rotation the larger the force.

Imagine a disk just like the one here, which does NOT rotate. We roll a marble from the center to the edge, it moves in a straight line.

We do it again, only this time we let the disk rotate at a constant speed. Now if I am standing on the disk in the middle I don't notice this force because I am rotating at a constant velocity, but all of a sudden I notice that the marble is not traveling in a  straight line, but is now moving along a bended path. Right away I think there must be a force acting to cause this effect.  This fictitious "force" is the Coriolis force F_c

 The idea of the Coriolis and Centrifugal forces is that they are correction factors that do not exist in a non-accelerating "inertial" system, so we say that they are fictitious or pseudo forces. I am not completely comfortable about this.  I can't help thinking that by using this terminology and this view of inertial frames we are actually missing or misunderstanding the whole picture.

Ultimately, just about everything spins, or is a part of something that spins, so the universe is in general a non-inertial frame of reference and yet we try to do most of our work in an inertial frames of reference because, lets face it, the calculations are easier and they are a good every day approximation. By doing this though I think that we are closing our minds to something far larger and potentially revealing. The fact that it is more complex is our failing to interpret and describe it properly, in reality it is no more complex.