Here is another applet about circular motion.
It was designed to illustrate relation/constraint for circular motion: a=V[sup]2[/sup]/R.

[color=red]Red[/color] arrow is the instance velocity V(t),
arrow with color "[color=#f0f]magenta[/color]" is V(t+dt)
The [color=blue]blue[/color] arrow is d\vec{V}=\vec{V}(t+dt)-\vec{V}(t) which is always pointing toward the center.
with  d\theta=V*dt/R ,
so It's length |d\vec{V}|=V d\theta=V* V*dt/R,
so \frac{d\vec{V}}{dt}=\frac{V^2}{R}

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