For uniform circular motion prove that linear velocity v=rw
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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
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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.
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