Question

For uniform circular motion prove that linear velocity v=rw

Answer 1

Answer:

You're moving in a circle of radius r, so the distance you travel in one full trip round the circle is 2.pi.r and you're doing it in one time period, T

speed, v = distance/time = 2.pi.r/T

w = angular speed, and you complete 2 pi radians in time T, so w = 2pi/T

Answer 2

Answer:

First let's prove it by scalar, then we can move for vector. ... consider uniform circular motion, and the plane of motion is x-y. r = r

You're moving in a circle of radius r, so the distance you travel in one full trip round the circle is 2.pi.r and you're doing it in one time period, T. speed, v = distance/time = 2.pi.r/T. w = angular speed, and you complete 2 pi radians in time T, so w = 2pi/T. so v=rw.