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Consider a car that travels around a circular test track of radius r.
v = ρ(dθ/dt) et a = (dv/dt)et + (v2/ρ)en
The speed remains constant. The acceleration remains constant. The radius remains constant.
We can rearrange the n-t equations for circular motion.
v= r(dθ/dt)
a = (dv/dt)et + (v2/r)en = r(d 2θ/dt 2)et + r(dθ/dt) 2en