I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match.
A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The total mass of the hemisphere is "M". Please refer to the attachment for the figure and my full attempt.
The solutions elsewhere use distance from the center of the hemisphere as a variable.
Where have i gone wrong?
y(cm) = ∫y dm / ∫ dm = 1/M (∫y dm)
The Attempt at a Solution
Please refer to the attachment.
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