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    Whats the easiest way to go by questions like this?

    = Find c.g from center of semicircle?

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    You should be used to finding the centre of mass by setting up a system of coordinates, and using:

     \displaystyle\sum m_ix_i = \bar{x}\displaystyle\sum m_i

    It is often useful to choose the origin of your coordinates to be the point mentioned in the question - in your case, set up the coordinates with the origin at the centre of the semicircle. Hence, you should then find that, after figuring out the centre of mass  G (\bar{x}, \bar{y}) , then its distance from the point in the question, now the origin of the coordinates is just:  \sqrt{\bar{x}^2 + \bar{y}^2} .
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    I haven't done this for a while but I think the knowledge that the shape is symmetrical will help (as the centre of mass will be slap bang in the middle (you just have to find the vertical distance from the centre of the semi circle now)...if this is a uniform shape - which it looks like)
 
 
 
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Updated: February 7, 2010
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