regarding the pendulum acceleration Ludwik Kowalski wrote on Wed, 24 Oct 2001
03:04:52:
"In other words, the NET FORCE, and thus the acceleration,
is zero at the bottom and non-zero at an angle, large or small."
The net force at the bottom is *not* zero because the pendulum bob is changing
direction (a circular path). Hence there must be a net force acting, in this
case the net force = tension - weight. So the tension force has greater
magnitude than the weight of the pendulum bob. Tangential acceleration at the
bottom is indeed zero but normal acceleration is not.
A few years ago the very same question was posed in the International
Baccalaureate (IB) physics exam. If I remember correctly, less than 10% of all
IB physics candidates got it right. I have to confess that my students had
difficulties with the question
as well :-).
This question has been used in physics education research by prof. Reif. He has
written a wonderful book on introductory mechanics (Reif 1995). He decribes a
nice method to find out direction of acceleration at any point of a pendulum
path.
In fact, the method is essentially the same that is used in deriving the
formula for normal (or centripetal) acceleration.