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Re: acceleration



Perhaps it would be more helpful to say:
The scalar acceleration is the forward (tangential to the velocity vector)
component of the acceleration vector.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.velocity.net/~trebor
trebor@velocity.net
----- Original Message -----
From: "John S. Denker" <jsd@AV8N.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, November 20, 2003 8:19 PM
Subject: Re: acceleration


On 11/20/2003 07:17 PM, SSHS KPHOX wrote:

>> -- The scalar acceleration has to do with speed. Speed is the
>> forward component of velocity.
>
> I am accustomed to velocity having components, x and y or tangential
> and radial

OK.

> but forward?

Why not? If we can define the forward direction,
we can project off a component in that direction,
nicht wahr?

> Is that in the instantaneous direction of the vector?

Yes.

> Will that not be differentially different in the next
> differentially different time?

Yes, it will be different.

> My limited understanding has speed as the "magnitude" of the
> velocity.

It's provably synonymous.

For any vector v (velocity vector or otherwise) that
happens to point in the forward direction (i.e.
aligned with the velcotiy, as discussed above), we
can write

|v| = sqrt(v dot v)
= sqrt(|v|^2)
= (v dot v) / |v|
= v dot (v / |v|)
= v dot (unit vector in the fwd direction)
= forward component of v.

Vectors are tricky in polar coordinates, because the
"radial" direction changes from place to place.

Trying to calculate things in terms of |v| is similarly
tricky, indeed trickier, because the notion of "forward"
is so changeable.