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**r**= rcosθ

**i**+isinθ

**j**=rcosωt

**i**+rsinωt

**j**and differentiating twice. Since ω is constant we get

**a**=-ω[itex]^{2}[/itex]

**r**.

I've started looking at non-uniform circular motion where there is also the tangential acceleration vector component. I'm told that the component of acceleration directed towards the center of the circle has magnitude v^2/r, but I don't believe the original proof works because we assumed ω is constant, and now it isn't. Can this type of proof be made to work still?