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Question

Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii R1 and R2 (figure 9-E5).

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Solution

ycm=y dmM

or dm=Mπrdrπ(R22R21)2

=M(R22R21)2dr

ycm=R2R1(2rπ).M(R22R21)2.rdrM

=2π(R22R21)2R2R1r2dr

=2π(R22R21)2[R32R313]

=4(R21+R1R2+R22)3π(R1+R2)


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