Question

(A) Show that the position of a particle on a circle of radius R with center at the origin (x=0,y=0) is given in unit vectors by r=cosθi+sinθj, where θ is the angle of the position vector with the x axis.

Answer 1

B) If the particle moves with constant speed v and period T, starting on the x axis at t=0, find an expression for θ in terms of the time and T.

Answer 2

C) Differentiate the position vector twice with respect to time to find the acceleration and show that it is the centripetal acceleration, whose magnitude is given by equation (a=(v^2)/r) and whose direction is toward the center of the circle.