(a) Show that the speed of the particle is (b) Use a graphing utility in parametric mode

Chapter 12, Problem 46

(choose chapter or problem)

Circular Motion In Exercises 45-48, consider a particle moving on a circular path of radius b described by \(r(t)=b \cos \omega t \mathrm{i}+b \sin \omega t \mathrm{j}\), where \(\omega=d u / d t\) is the constant angular velocity.

(a) Show that the speed of the particle is \(b \omega\).

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

Text Transcription:

r(t)=b cos omega t i + b sin omega t j

omega=du/dt

b omega