On 11/19/2003 05:52 PM, Matt Jusinski wrote:
>
> If the scalar acceleration is zero locally, and the
> speed is locally zero, Why does a projectile fall back
> down?
This illustrates a useful general rule: ask a different
question, get a different answer.
-- The scalar acceleration has to do with speed.
Speed is the forward component of velocity.
-- Falling down has to do with the vertical
component of velocity.
These are two different concepts. At the peak of a
parabolic arc, these two projections are perpendicular
so in some sense have precisely nothing to do with each
other. The velocity vector is changing. The downward
component is changing. The forward component is *not*
changing. No problem.
> It seems to me that scalar acceleration is not much
> help in explaining most common phenomenon.
Once again: ask a different question, get a different
answer.
-- If the question is what is the best way to analyze
the details of the dynamics of a thrown object, the
answer usually includes the vector acceleration.
-- If the question is what is going through the
minds of intelligent non-physicists when they say
the acceleration is zero at the top of a parabolic
arc, the answer may well be scalar acceleration.
There are many questions for which vector acceleration
is the right answer. There are also many questions
for which scalar acceleration is the right answer.
=====================
I do a lot of writing, and I try to use words carefully.
I try to make everything nitpick-resistant. Once when
writing a book I tried to impose the rule that "in
this book, the word acceleration always refers to
vector acceleration" ... but I found it was impossible.
There are just too many situations where the scalar
acceleration crops up, and no matter how hard I tried
to find circumlocutions (e.g. "speeding up" instead
of scalar acceleration, and "slowing down" for
deceleration) there situations where I just gave up
and used the natural, normal, centuries-old notion
of acceleration ... meaning scalar acceleration.
I know a big part of the agenda of a intro physics
course is to teach people about vector acceleration.
I know this is hard. But pretending scalar acceleration
doesn't exist would be a step in the wrong direction.
Even if I thought scalar acceleration were the enemy,
I would say: know thine enemy!
But it's not the enemy. If it were intrinsically bad
it would have been killed off by now. The problem is
that it is sufficiently useful and sufficiently well
established that it will never die out. It is a
cousin and a neighbor the vector acceleration. So
for pedagogical reasons as well as technical reasons
my advice is: know thine neighbor!