A particleĀ PĀ moves with constant angular speedĀ ĻĀ around a circle whose center is at the origin and whose radius isĀ R. The particle is said to be inĀ uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the pointĀ (R,0)Ā whenĀ t=0. The position vector at timeĀ tā„0Ā isĀ r(t)=RcosĻtĀ iĀ +Ā RsinĻtĀ j.
(a) Find the velocity vectorĀ vĀ and show thatĀ vā
r=0. Conclude thatĀ vĀ is tangent to the circle and points in the direction of the motion.
(b) Show that the speedĀ |v|Ā of the particle is the constantĀ ĻR. TheĀ period TĀ of the particle is the time required for one complete revolution. Conclude that
T=2ĻR/|v|=2Ļ/Ļ
Ā