Why Do We Include Coriolis Acceleration in Motion Equations?

[zezima1]

Let aS denote the acceleration of an object as measured in a reference frame S that accelerates relative to another reference frame with an acceleration aI. We then have that the absolute acceleration of the object as measured in an inertial frame of reference is given by:
a = aS + aI + aC
where a is the socalled coriolis acceleration, which I have a lot of trouble getting around. Can anyone give me some intuition on why you add this term other than the mathematics behind it. For me you could just as well add the accelerations like you add velocities but then of course, I don't really know if I have a lot of intuition as to how acceleration behaves as seen from different frames of reference.

 

[Ken G]

I think the problem is that there is a big difference between a reference frame that is "accelerating", which suggests a spatially fixed acceleration throughout, and one that is "noninertial", which allows the acceleration to vary with location. The classic example of a noninertial frame is a rotating frame, which is a frame in which you will see things like coriolis and centrifugal accelerations. These accelerations are not everywhere the same in either magnitude or direction, so are both to be distinguished from simple translational accelerations of the entire frame. In practice, the only accelerating frames you need to understand are those with a spatially fixed acceleration (if the observer is accelerating) and those that are rotating (if the observer is rotating). That's all an observer can (instantaneously) be doing that would affect Newton's laws.

 

[zezima1]

okay but if the coriolis acceleration is only something which occurs in a rotating frame, why don't the equations of motion account for the fictitous forces that occur in a linearly accelerated frame - e.g. being pushed back in a car etc.

 

[Ken G]

They do, that's the aI in your original expression-- but that kind of force is not called the coriolis force.

 

[PJC01]

I can provide a response to the concept of coriolis acceleration. First, it is important to understand that the coriolis acceleration is a fictitious force that appears to act on objects in a rotating reference frame. It is not a real force, but rather a mathematical construct that helps us describe and understand the behavior of objects in rotating systems.

To understand why we add the coriolis acceleration term in the equation, it is helpful to consider an example. Imagine a person standing on a rotating turntable. From their perspective, they are not moving and there is no acceleration. However, from an outside reference frame, we can see that the person is actually accelerating towards the center of the turntable. This acceleration is caused by the rotation of the turntable, and it is what we call the coriolis acceleration.

In the equation provided, aS represents the acceleration measured by an observer in a non-inertial (accelerating) reference frame, while aI represents the acceleration of that reference frame itself. The coriolis acceleration term, aC, is added to account for the additional acceleration caused by the rotation of the reference frame.

In essence, the coriolis acceleration is a way to account for the fact that an object's motion appears different when viewed from different reference frames. It is necessary to include this term in the equation in order to accurately describe the motion of objects in rotating systems.

I hope this provides some intuition on why we add the coriolis acceleration term in the equation. It may seem counterintuitive at first, but it is a crucial concept in understanding the behavior of objects in rotating systems.