OT: LOTD and a Q for the brainiacs

As the first cartoon points out, we don't live in a Newtonian frame.

I think the term 'centrifugal force' should be changed to 'centrifugal reaction'. The human brain needs to explain everything felt in terms it can easily understand. CF has been one of my pet peeves for 44 yrs now. phil k.

Yes.

The hard thing about coordinate transformations is keeping everything straight.

First of all, if you have a vector V in one coordinate system, you can express it as V' in another coordinate system, but it's still the same vector. (Relativity makes this a bit harder, but it's really the bookkeeping that'll cross you up if you aren't careful.)

Say you have a vector V, expressed in a frame rotating with an angular velocity _Omega_. The vector might be the velocity of a marble sliding frictionlessly on a turntable, measured in rotating Cartesian coordinates. Since the motion is frictionless, in the lab frame it moves in a straight line at a constant speed, but in the rotating frame it accelerates.

The rate of change of a vector _V_ in a frame rotating at Omega is

d_V_/dt = d_V_lab/dt + _Omega_ cross _V_

(the vector cross product). The cross product of two vectors is another vector, perpendicular to both of the operands and having length equal to the product of their lengths times the sine of the angle between them. (Wikipedia will have the exact expression for it.)

When you take that apart into its radial and tangential components, you get centrifugal and Coriolis acceleration, respectively. If you don't try to stop the marble from sliding, no force is required, and it just does what it does. If you want to keep it in one place, however, you have to exert real force to counteract the centrifugal and Coriolis forces.

(This is from memory so I may have a sign backwards someplace.)

Cheers

Phil Hobbs

What's you definition of "force"?

Lighten up. Yeah, "centrifugal force" not technically correct, but it is useful. "Centrifugal force will throw the water off the grinding wheel" is PERFECTLY understood. That's what really matters in most contexts. Science requires rigor, day-to-day conversation does not.

Bob

I seem to remember mass*acceleration

My memory is real foggy on this but Newton invented calculus to describe position, velocity, and acceleration. I do remember you take the derivative of position to get velocity and the derivative of velocity to get acceleration. Newton was bothered by the dM/dT term in addition to the dV/dT term in the proof of this. A few years later a fella named Einstein came along and proved the change in mass term is also there.

Karl

In physics, a force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape.

The third of Newton's laws of motion of classical mechanics states that forces always occur in pairs. Every action is accompanied by a reaction of equal magnitude but opposite direction. This principle is commonly known in the Latin language as actio et reactio. The attribution of which of the two forces is action or reaction is arbitrary. Each of the two forces can be considered the action, the other force is its associated reaction.

wiki

also...

A particularly subtle common mistake is to confuse the forces that cause action and reaction with the actual action and reaction.

This mistake comes about partly because the very definition of force is all about a mass experiencing an acceleration, and there is an assumption that an object's entire mass is always the entity that is accelerating. Actually, though, when an object experiences a common impact-type of force, at the instant the force is applied, only the atoms and molecules at the surface of the object begin to accelerate. These push on neighboring atoms and molecules, and a mechanical wave of force propagates through the body of the object at the speed of sound in the substance of the object. Typically, for ordinary objects, the entire mass of the object experiences the applied force in a thousandth of a second or less,[citation needed] which makes it easy to assume (especially in eras before modern instrumentation existed) that the whole mass of the object is instantly experiencing the force. From this description, however, it should be obvious that during the time that the wave of force propagates through an object, only part of the mass of the object is accelerating, not all of it. One result of this is that when two significantly different masses interact, even though the force between them, that causes action and reaction, happens perfectly simultaneously, the two masses may not fully respond/accelerate/act/react simultaneously.

I dimly recall seeing a proposal to recalibrate various records at the 1968 Olympic Games, to "correct" them for Mexico City's 2km altitude. Nothing ever came of it, so far as I know.

It falls right out of the equations. (or geometery) Acceleration is the change in the velocity vector. The velocity vector can change in both magnitude and/or direction. (Stomping on the brakes versus whipping around a corner.) If you assume circular motion you can draw a picture of the velocity vector at two near by points in time. (I think of spokes on a wheel with little velocity arrows stuck onto the spokes.) Then you have subtract the vectors. (This would be so much easier if you could come over here and I could draw pictures.)

Anyway it's pretty standard freshman physics stuff. Do you have an old physics text book?

George H.

Well, do the coordinate substitution and find out.

(I believe it's Vx' = Vx + kr sin theta, Vy' = Vy + kr cos theta, where theta = arctan y/x, r = sqrt(x^2 + y^2))

The thing that, when you try to push a wall with your hand, determines how the wall knows how hard to push back? ;-)

Cheers! Rich

But what if it's not making any change, like, say, a spring scale with a one-pound weight sitting there, and it's indicating a pound, and just sitting there?

What do call the stuff that's causing the pound weight to hold the spring at 1 lb. deflection?

And in the classic "wall pushes back", there's no motion, what do you call the stuff that's doing the pushing? (besides "triceps," of course. ;-) )

Thanks, Rich

Yes. If you choose the right coordinate system to examine the problem.

Namely an R, theta, phi with its axis centred on the axis of rotation. And you could make them arbitrarily more incomprehensible by choosing the wrong coordinates system and point of origin.

Try it for yourself put (x = Rcos wt, y = Rsin wt) work out x", y"

Put simply the centrifugal force and coriolis forces are fictitious forces that someone at rest in a rotating frame of references feels acting upon them when they try to apply Newtons laws naively.

In the old days when radar tehnicians sat in sheds behind the early WWII radar antenna rotating with them to tune them up they had to be careful when reaching for a spanner in that frame of reference. My first supervisor had first hand experience.

Same as some of the fairground rides that spin up and then tip over. The force you feel from the rotation is outward and real enough to overcome gravity. Spinning up spacecraft to provide some form of artificial g is under consideration but the radius needs to be quite large to avoid nuisance effects on the astronauts.

Centripetal force is a piece of high school political correctness in physics and adds nothing to the understanding. Any more than insisting on IUPAC names for common organic chemicals does in chemistry.

Regards, Martin Brown

Oh, I get the concept - actually you didn't even need to give the spokes and little arrows image. :-)

But at that point, I get it conceptually, and kinda in a "feeling" sort of way, but the math is way way beyond me.

In elementary and high schools, I was always pretty good at arithmetic, all the way up to derivatives. They had time to hint at calculus in HS, but that was about all.

Then I went to college and hit vectors and integrals and gawdknowswhat, and it was like a brick wall.

So I dropped out and since this was 1968 with the draft in full swing, I dodged the draft by joining the Air Force. They made me an electronic tech, which was handy, because I'd been an electronics whiz kid since my brother built the Boy Scout crystal set when I was about 6, and I was captivated. :-)

Cheers! Rich

No, but I do have access to a copy of "Ringworld." ;-)

Cheers! Rich

Seems to me that no, you wouldn't. You have to define a frame of reference (down is down, up is normal) so there would be no rotation. The only way to generate a 'rotating system' would be to invoke Newton's laws on a space that was rotating with respect to your frame of reference. So Newton's laws would be the same as when you are observing a turning wheel...centripetal acceleration and no centrifugal force.

What's doing the pushing? An acceleration. Actual movement is not a requirement.

Between your Niven and my Asimov's _Understanding Physics_, we might get something done. 'course, mine's still in my 18' tall stacks of "To be read" books...

-- Ask not what the world needs. Ask what makes you come alive... then go do it. Because what the world needs is people who have come alive. -- Howard Thurman