Question

How is the formula v=rω derived?

Answer 1

Thanks to @GRrocks for guiding me through. This is how v=rωv=rω is derived:

velocity=displacementtimevelocity=displacementtime

v=dsdtv=dsdt

Since our displacement/distance is the length of the arc which is made by the angle dθdθ: s=rdθs=rdθ

v=rdθdtv=rdθdt

Since rr is constant: v=rdθdtv=rdθdt

dθdt=ωdθdt=ω

Therefore! v=rω


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