What makes the inertial reference frames “proper”? Sometimes it’s a lot easier to work in the rotating frame, and if you know what you’re doing, it still gives the right answer. What’s so improper about a method that’s easier to use and consistently gives the right answer?
When you’re “pulling” on the end of the piece of duct tape, the surfaces of your fingers are pushing against the surfaces of the piece of tape.
If on the other hand you make a loop of tape, with the stickiness outwards, stick it onto a smallish object on your desk and then lift said object with the use of the tape and ask: “What’s happening in the tape/object interface?” That’s hard to explain without pull, so its obviously outside of the bounds of what we’re discussing.
You would need reciprocals to achieve division with multiplication. And to find the reciprocal you have (or someone else has had to if you use tables) divide one by the number in question.
I would go further and say that it’s actually rather pretentious and silly.
In the case of ‘centrifugal’ force, there is a real and measurable force that has been named ‘centrifugal’.
The fact that some people have at some time said incorrect things about the nature of that force does not mean either that it does not exist or that it should not be called by that name. (Unlike a case where there is another force that has the name ‘xxx’ and that name is being misapplied.)
Well, that’s just like saying you would need negation to achieve subtraction with addition. And to find the negation you have to subtract from 0 the number in question.
But it’s all a bit quibbling. I can contrive contexts in which trying to isolate one or another basis of simple operations from which all the others of interest can be constructed might potentially be useful, but such contexts would be niche at best. For the most part, there’s no use in worrying whether negation precedes subtraction or subtraction precedes negation or multiplication by a particular constant “-1” precedes them both, or if -1 only arises as the square root of a complete revolution or square of a 90 degree rotation, or whatever. The relations between them are interesting, but trying to assign priority is less so.
True for humans but computers can change positive to negative without subtracting anything. So, internally a computer can subtract without ever performing a subtraction per se (
).
OTOH, it can’t perform a division without actually going through the process of division.
But within that reference frame, the force is very real, measurable, and will crush you like a bug if you don’t stay in your seat with your seatbelt fastened until the centrifuge comes to a complete stop at the gate. It is no different from the thrust you feel when in a vehicle accelerating along a straight line, and the acceleration is indistinguishable from acceleration due to curvature in a gravity field, or electromagnetic attraction, or any other fundamental force for both classical mechanics (D’Alembert’s principle) and relativistic mechanics.
Rotating planar frames about a fixed axis are somewhat special in that they contain additional components that are orthogonal to the reactive centrifugal force that let you know that you’re in a rotating frame; the Coriolis component (normal to the plane of rotation), and for non-uniform rotation, the azimuthal or Euler component, which is in opposition to the instantaneous tangential direction of motion in plane, but the forces are, again, real and measurable for anyone within that plane, even though they may appear “fictional” to someone outside the rotating system who is viewing that system as being a quasi-static rigid body.
Inertial frames are referred to as privileged insofar as you don’t need any kind of state variables to describe them other than to say that they’re inertial, but that doesn’t make the forces arising from the dynamics of non-inertial systems somehow less real than forces generated by fundamental fields, and indeed, we may eventually find that gravitational forces and inertial forces are actually two different emergent behaviors of the interaction of mass-energy with an underlying field, as abstracted in general relativity by the metric tensor on a pseudo-Riemannian manifold. In other words, resistance to changes in motion (inertia) is the same as resistance to deviating from a circular orbit around a planet.
In reality there are no inertial reference frames! Everything we know and see–even planets, probes in interplanetary space, and the Solar System and Milky Way Galaxy itself–are all rotating and accelerating in several ways, including streaming in the general direction of the Hydra-Centaurus Supercluster as several hundred km/s. Fortunately, the gradient of those fields is small enough that we’re locally flat and for everyday purposes only have to consider the Earth’s gravitation (and limited effects of that of the Sun and Earth’s Moon).
Stranger
As I understand it, computers mostly do division through interpolating on a huge lookup table of reciprocals of the numbers between 1 and 2. The infamous arithmetic bug on the first generation of Pentium chips was an incorrect value on that lookup table.
They are still going through a process of division (which is why I used that term rather than just saying ‘dividing’).
The point is that a computer does not need to have any circuitry to perform subtraction as it can simply obtain the twos complement of the number to be subtracted and add. (That doesn’t mean that all computers have to use that approach but they can.)
On the other hand they have to have to have specific, non trivial, processes for division since you can’t obtain a reciprocal in such a simplistic manner.
The three things you need to know to be a Civil Engineer:
[ol]
[li]Shit flows downhill;[/li][li]You can’t push a rope;[/li][li]Payday is Friday.[/li][/ol]
Well, that depends on what representation of numbers you use. In IEEE floating point arithmetic, sure: negation is trivial (flip one bit), reciprocation is much more difficult (and usually accomplished with the aid of a precomputed table, as Chronos noted). But in rational arithmetic, representing rational numbers as pairs of twos-complement integers, reciprocation and negation are both easy. In rectangular representation, adding complex numbers is simple, multiplying them is a bit of work, and exponentiating them is a whole load of work; in log-polar representation, multiplying is simple, exponentiating is a bit of work, and adding is a whole load of work. These things always depend on representation.
But, anyway, my point was only, as I said, that it is often, and particularly in this case, silly to gloss “Y can be described in terms of X” as “There isn’t really any such thing as Y”.
With which I absolutely agree. 
How do you feed a rope through a hole?
He was pulling your leg.
Carefully.