A particle undergoes uniform circular motion This means that it moves in a circle of radius R about 

A particle undergoes uniform circular motion. This means that it moves in a circle of radius R about the origin at a constant speed. The position vector of this motion can be written as r(t) = Rcos(ωt)i + Rsin(ωt)j Here, analogous to the simple harmonic motion problem of HW, ω is the angular frequency and has units of rads = 1s. It can also be written in terms of the period of the motion as (a) Show that the particle resides at a distance R away from the origin at all times. That is, show that the magnitude of r(t) is R for all times. (b) Calculate the velocity vector of this motion. How is the velocity vector oriented relative to the position vector For example, parallel, perpendicular, or at a particular angle relative to the position vector. (c) Calculate the speed of the particle for all times. Show that the speed can also be written as 2πRT. (d) Calculate the acceleration vector for this motion. How is the acceleration vector oriented relative to the position vector For example, parallel, perpendicular, or at a particular angle relative to the position vector. (e) What is the magnitude of the acceleration vector for all times Show that it can be written as ω^2R.
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