Posted by Chris on Sunday, June 10, 2012 at 5:44pm.
x1=0, y1=0, x2=2m, y2=0.
R=4 m, r=1 m.
y(c.m.) =0
x(c.m.) = (A1•x1 –A2•x2)/(A1-A2)=
=(A1•0-A2•x2)/(A1-A2)
= - πr²•2/π(R²-r²) =
= - 1•2/(16-1) =2/15 = - 0.133 m
Center of mass x=- 0.133 m, y = 0
Hint: If you take the equation for the cente of the mass, and you multiply that by the total mass, you get:
Integral of rho(r) r d^3r
This satisfies the superposition principle, the result for a density function rho1 + rho2 is the same as that for rho1 and rho2 seperately and then added together.
This means that you can add up the what you get for a disk without a hole to what you get for a hypothetical disk of negative mass. You then divide the result by the total mass.
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