But, in fact, why don’t I set the record straight here. I don’t care if you want to talk all day about a non-intertial frame. I certainly wasn’t, so if you were, then I’m sorry for thinking you’d stay on track.
I’m sorry, but that’s bullshit any way you slice it. There is a net accelleration toward the center, of this we seem to agree. There can be no net anything in one direction unless there is another, lesser something in another direction. You want to consider only forces, fine, be my guest—the math is the same, and we will describe the same circular motion. When I study motion, I tend to look at and do the math with accelleration, which is the result of a force acting on a mass.
We are moving in a (rough) circle. The accelleration due to gravity is too much to do this with the radius and velocity in question. There must be some component vector that counters this. You want to work only with forces? Fine. Mathematically equivalent since F=m*a. I’m going to work with accelleration.
If you disagree, show me the math, and show me why I am wrong there. Please. Otherwise, your childish ranting will be wasted on deaf ears.
Nametag says: << I will concede, though, that you are less ignorant of physics than you are of English. >>
erislover responds: << … your childish ranting will be wasted on deaf ears. >>
Administrator claps his hands, VERY LOUD, to attract attention. OK, children, enough of that. Name calling is NOT permitted in this forum. If you want to do name-calling, go to the forum called the BBQ Pit. This forum is limited to polite discussion or debate, and taunts such as the above are not permitted.
Consider this a formal warning. Play nice, or play elsewhere.
OK, hopefully I can clear up some of the confusion here.
erislover, it’s specifically net force on an object that is equal to its acceleration times its mass. Acceleration is the rate of change of velocity; an object has only one acceleration. Of course, for each force acting on the object, there is an acceleration that would result if that force alone were acting on the object, but to casually speak of one of these as a real “acceleration” is a misuse of the term. The only acceleration is “net” acceleration. There are, however, forces other than the net force, which is really just the sum of the actual forces acting on the object. And that’s why we should properly talk about forces instead of accelerations on an object in a discussion like this. You’re right about the mathematical equivalence of the descriptions (for an object of constant mass), but, well, it’s a semantic thing.
Now then, Nametag, you said
Ahem. When a ball, thrown upwards, reaches its maximum height, it has a velocity of zero, but still experiences a net force and an acceleration. A stationary object has no velocity by definition, but it doesn’t follow that it’s not accelerating; a nonmoving object can have an acceleration. I’ll grant you, you could
(re)define “stationary” so that it only refers to something that has no velocity for more than just one instant, which is clearly what you’re talking about, and which would be reasonable enough. But that would be weaseling, in my view.
But even worse, you said
To say that someone standing on the Earth is accelerating downward is almost as bad as saying that (s)he is accelerating upward. Technically you’re correct; there’s a net downward centripital force that keeps us moving in a circle around the Earth, which is spinning. However, in this case, I think that the intuitive view is to use the reference frame of the person standing on the Earth. (Yes, I know that that contradicts what I said before about the inertial frame being assumed “correct” by convention. Look, it’s all a matter of context. No, really, it is! Shut up.) From that view, you seem to be misusing the term “acceleration” in the same way as erislover later did, and I think that this may have contributed to his/her confusion about the use of that term in the first place. Besides, if you really want to look at things non-inertially, you’ve also got to consider that not only is the Earth spinning, it’s going 'round the sun, and the solar system itself is orbiting around the center of the galaxy, etc.!
Oh, and for completeness, I guess I should add that I’m assuming that we are talking about someone standing on the ground, not in free fall. That was what we were discussing, right?
So, given the right assumptions, I think everything you said was technically correct. But since you didn’t explain those assumptions, you stated a few things in a fashion that some people may have found misleading. So ease up, OK?
Well, I’ve never heard this. I can live with it, no problem. I think in terms of the math, and the math often uses component vectors.
For the record, say you were studying a rocket propelled sideways along the earth and you knew the force the rocket put out. Why would the one component vector of accelleration be less real than the net accelleration from the addition of the vectors? Is this a stupid question?
Oh, I just noticed that erislover said the following:
"quote:
There IS, however, another force acting on most objects, the force exerted by the Earth itself, equal and opposite to the force that we exert on it.
Sorry, no. If this were true we wouldn’t travel in a circle, we’d fly right off the earth. Why don’t you check my math?"
That’s exactly correct, if you’re using the solar system as your frame of reference; gravity is somewhat stronger than the normal force (the force that keeps solid objects from moving through each other), and this centripital net force keeps us moving around the Earth. Only from the non-inertial frame of someone standing on the Earth are the two forces equal and opposite.
"quote:
When viewed in an INERTIAL frame of reference that is stationary with respect to the Earth’s center of rotation, this force is slightly less than, but still opposite to, the force of gravity, and there is a net CENTRIPETAL acceleration – that is, DOWN.
Yes, a net cetripetal accelleration. Can you tell me why you use the word “net” without proving my point?"
Indeed. Unless you are (mis)using the term “acceleration” as erislover did, “net acceleration” is redundant; in fact, it implies that there are “component” accelerations.
In the future, Nametag, try to be more consistent in the way you talk about something. Even if there are two equally correct but conflicting ways of describing something, switching between the two without notice can lead to (apparent) contradiction.
It’s not that the component vectors aren’t “real”, but a component of the object’s acceleration isn’t “an acceleration of the object”, only the “net” acceleration is. Or to put it another way, “net acceleration” is redundant.
At least I hope I’ve got that right. I mean, I’m gonna look pretty stupid going on about it like I did if I’m wrong.
In all my physics and dynamics and engineering classes, I never encountered anyone making a big deal about it. We talked about component accelerations all the time. When breaking down forces by vectors, we also broke down accelerations by vectors. An object is seeing independent accelerations, it’s just they sum vectorially. Same difference.
erislover is correct in this. The force exerted by the Earth on any object is exactly equal in magnitude (and opposite in direction) to the force that object exerts on the Earth. This is Newton’s Third Law, and it is true regardless of the relative motion of the Earth and the other object, or of the reference frame used.
The total force of the Earth on an object has two parts: A gravitational part and a contact-force part. If we neglect the rotation of the Earth, and look at an object resting on the surface, it is also true that these two parts to the force are equal in magnitude and opposite in direction. This is a special case of Newton’s Second Law (F[sub]net[/sub]=ma, where a = 0). Therefore, the Earth exerts zero net force on such an object. If we do not neglect the rotation of the Earth, and consider an object resting on that surface, then the gravitational force must be slightly larger than the contact force, for a small net force downwards, which is keeping the object moving in a circle about the center of the Earth. I think that’s what you’re referring to.
Chronos, I believe that’s my point you’re agreeing with.
Devil’s Advocate, of course “net acceleration” is redundant. You have to do that when people don’t get it the first time. Moreover, a broad definition of "stationary as “not moving” is not weaseling; that term is reserved for narrow definitions such as “having reached an instantaneous velocity of zero during the ballistic course of flight of an obviously moving object.”
Obviously, acceleration can be separated into component vectors; had the words “vector” or “component” been used in the first place, there would be no argument. But both Erislover and I were addressing CurtC’s erron:eous contention that
It’s clear that CurtC’s post is referring to the actual acceleration experienced by an object, not some smaller component of it. I didn’t immediately catch on that erislover’s one-line quip was about the acceleration component generated by the Earth’s contact force. It’s now been made abundantly clear that this is the case, so erislover’s reply was not wrong, but it was sloppy and irrelevant.
I think in terms of the math, and the math often uses component vectors.