Chapter 3, Problem 92P

(a) Show that the position of a particle on a circle of radius R with its center at the origin is $\stackrel{\to }{r}$ = R(cos θî + sin θĵ), where θ is the angle the position vector makes with the x-axis. (b) If the particle moves with constant speed v starting on the x-axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.