Bob Sciamanda has given a correct response. But I find some students
don't understand why we need to slant the coordinate system to get the
correct answer. Why can't we just use a coordinate system that is
aligned with gravity for this problem? The answer is that we can, it is
just a bit more tricky to know what the acceleration is.
In David Albineri's original question, the problem of correctly
identifying the acceleration for the gravity-aligned system is manifest.
The problem with this free body diagram is not the diagram, but the
assumption that the vertical acceleration is zero. The vertical
acceleration in this diagram is -gsin^2(th). Where in the world did
this come from?
As Bob points out, the first key is realizing that the centripetal
acceleration is zero when the velocity is zero. In the slanted
coordinate system this simply means a(y) = 0. In the gravity aligned
system it means (a)dot(T) is zero.
I have worked this out in detail and placed it in an Acrobat PDF file
posted at the following address:
www.bluffton.edu/~edmistonm/swing.pdf
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.