Question

The Position Of A Particle Moving In The Xy Plane Is Given By R= [2.0*cos(3.0t)i+ 2.0*sin(3.0t)j] Where R Is In Meters And T Is In Seconds A) Show That This Represents Circular Motion Of Radius 2.0m Centered At The Origin.

Answer 1

Step-by-step explanation:

We can prove that this is a circular motion if we demonstrate that the norm of the vector is independent of time. Hence we have

`R(t)=2.0cos(3t)\hat{i}+2sin(3t)\hat j\\\\|R(t)|=√(4cos^2(3t)+4sin^2(3t))\\\\|R(t)|=√(4(cos^2(3t)+sin^2(3t)))\\\\`

but cos^2(3t)+sin^2(3t)=1. Thus we obtain

`|R(t)|=√(4)=2`

The norm is independent of t, thus, the particle describes a circular motion

Hope this helps!!