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The simplest way to show that the motion is
circular is to show that the dot product of the
velocity and acceleration vectors is constantly
zero for all theta. This should be done
algebraically, but just for fun we’ll see if we can
do it with the calculator too.
Use X2 & Y2 to hold the velocity and X3 & Y3
to hold the acceleration, pressing after
each one to perform the differentiation.
Now we go to the Function aplet and enter the
formula for the required dot product as
X2(X)*X3(X)+Y2(X)*Y3(X).
If we now switch to the NUM view, we can see
that this function is evaluating to zero for t = 0,
1, 2, 3…. Of course this is not the same as a
proper algebraic proof but you wouldn’t want
the calculator to do all the work would you?
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