Consider a particle moving on a circular path of radius b described by r(t) = b cos ωti + b sin ωtj, where ω = du/dt is the constant angular velocity.

(a) Show that the speed of the particle is bω.

(b) Use a graphing utility in parametric mode to graph the circle for b = 6. Try different values of ω. Does the graphing
utility draw the circle faster for greater values of ω?