Alan Baker wrote:
In article ,
VtSkier wrote:

Walt wrote:
VtSkier wrote:

Help me out a little more with VECTOR here.
I don't know that I can teach you vectors over the interwebs. Back when
I used to teach college calculus it would take most students the better
part of a semester to really "get" it. And without recourse to
mathematical notation, I'm kind of limited. Sorry, but it's kind of
like trying to teach skiing in a text only medium - you can only go so
far before you start sounding like foot to foot.
I actually took a calculus course once. It was taught
as a "pure" discipline and you were to use the rules
and apply them as taught. Nowhere was there any
explanation of WHY these rules were taught and WHAT
the math could be used for. IF I had been told that
the math was to describe motion and rate of change,
I might have found a reason to actually learn the stuff.

As it is, I excel in trig and geometry because I was
shown practical applications from the get-go.

It took two tries to pass calculus and the second time
I only passed because I had taken it before and the
instructor's first language was not English and he
graded on a curve in a class where NO ONE had a clue.

I hope your teaching was as patient and thoughtful
as your explanations here have been.

I still have one more, though, not entirely
related to the present post's discussion.

You said early on that TORQUE and WORK were
not the same thing at all except that they
shared the units used.

I still have yet to puzzle out what is so much
different between the two EXCEPT that direction
of the FORCE applied over a length has been
added to create TORQUE as opposed to WORK.

The concept of horsepower was originally
formulated on the basis of WORK, that is
moving a FORCE over a LENGTH in a given
period of time. Yet today we use TORQUE in
place of WORK for formulating HORSEPOWER
in a rotating engine.

In any case, whether it's TORQUE or WORK,
HORSEPOWER = 550 FT-POUNDS/SECOND.
The difference being that you would use
RPM (or more correctly RPS) for the TIME
component.

I'm sure there are mathematical reasons for
the answers to come out the same even though
the components are slightly different, it
still says to me that the concepts of WORK
and TORQUE while slightly different, are very
closely related. This I think was the beginning
of the discussion.

Yes, torque and work are very closely related. In SI units, Torque is
work done per radian of revolution (a radian is about 57 degrees) If you
apply a torque of 1 Newton-Meter and move through an angle of one radian
you have done 1 Newton-Meter or 1 Joule of work. If you apply a torque
of 1 Newton-Meter and move through a complete revolution, you have done
2*pi Joules of work. If you apply a torque and nothing moves, you do no
work.
So I guess that TORQUE can be analogous to WORK when there is
movement and it can be analogous to FORCE if there is no movement?

Sigh

No. TORQUE can never be analogous to WORK. TORQUE is the rotational
analog of FORCE.

It does *not* require there to be any movement of the system for there
to be torque, just as there doesn't need to be any movement of the
system for there to be a force applied in a linear motion system.

And if you know the torque and revolutions per minute you can calculate
the rate of work (i.e. power). Hence the familiar relationship between
torque, Horsepower, and rpm from automotive engineering.

To sum up:

Power is work per unit time
yes

Force is work per unit distance
no, work is force per unit distance

No. W = Fd.

Work is force *times* distance, and thus Force is work/unit distance.

Torque is work per unit angle
Yes, but if you say it this way, you have
strongly implied motion because WORK is
FORCE per unit DISTANCE. Yet you and Klaus
are convincing me that TORQUE can exist
without movement. See my question above.

No. He's implied that if there is *WORK* done then there must be *both*
TORQUE and rotation or FORCE and DISPLACEMENT.

See below. You can also say that TORQUE
is ENERGY per unit angle.

RPM is angle per unit time
Yes, which is why the horsepower equation
works with either work over time or torque
over RPS, the angles cancel each other so
the actual units match foot-lbs/second x 550

Wrong again. Horsepower isn't torque *over* RPM, it is torque *times*
RPM.

--------------------------------------------------

Actually I think I just got it here and it goes back
to my thoughts on potential this and that.

It's the difference between WORK and ENERGY.
WORK = FORCE x DISTANCE, yes?

ENERGY = FORCE applied to an object yet it doesn't move.

No. Utterly incorrect. Place a weight on a table: the table will exert
an upward force on the weight (if it didn't, gravity would continue to
move the weight downward) yet no energy is expended.

and there is no movement.

Trouble is, we don't have two different terms to
describe TORQUE with movement or without movement.

http://hyperphysics.phy-astr.gsu.edu/hbase/work.html

Because there is no need for one; just as there is no need for two terms
to describe force with and without movement.


Alan, I'm doing better here with Walt. At least he
has some patience with an old fart stuck in the last
century, maybe the century before.