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A ball is spun in a vertical circle on a string. A light is shining from the side of the circle so that a shadow of the balls motion is shown on a wall behind it. The shadow is simply a circle moving up and down in a straight line (I can't attach the image). The amplitude of the shadow is 0.5m and it takes 1s for the shadow to move from the bottom to the top and back. What is the angular velocity, tangential velocity, and centripetal acceleration of the ball?

a = v^2/r

w=2pi/T

v=rw

x=asinwt

a=-w^2asinwt

v=wAcoswt

v^2=w^2(A^2-x^2)

Well I'm guessing this is something to do with UCM being projected onto the diameter, as in https://www.physicsforums.com/archive/index.php/t-17536.html"thread. From there however, I don't really know where to start!

## Homework Equations

a = v^2/r

w=2pi/T

v=rw

x=asinwt

a=-w^2asinwt

v=wAcoswt

v^2=w^2(A^2-x^2)

## The Attempt at a Solution

Well I'm guessing this is something to do with UCM being projected onto the diameter, as in https://www.physicsforums.com/archive/index.php/t-17536.html"thread. From there however, I don't really know where to start!

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