Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: acceleration



(d/dt)|v| is undefined at the peak:
The limit from the rising side (-g) differs from
the limit from the descending side (+g).
Thus, the scalar acceleration is undefined
at the peak.

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org


-----Original Message-----
From: John S. Denker [mailto:jsd@AV8N.COM]
Sent: Wednesday, November 19, 2003 6:13 PM
To: PHYS-L@lists.nau.edu
Subject: Re: acceleration


I wrote:

Asking what is "the" acceleration at the peak of a
parabolic arc is at best ambiguous.
-- The scalar acceleration is zero. The speed
is locally constant at this point.
-- The vector acceleration is of course just g.

On 11/19/2003 06:47 PM, cliff parker wrote:

At what point isn't the speed locally constant?

At all other points (other than the peak of the trajectory)
the speed is not locally constant. "Locally" is shorthand
for "to first order".

To see this, calculate (d/dt)|v|. If you're feeling
lazy, look it up e.g.
http://mathworld.wolfram.com/Acceleration.html
(where beware s denotes arc_length, not speed).
Equation 6 is particularly elegant and easy to interpret:
(scalar acceleration) = (unit tangent) dot (vector acceleration)