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christikiki22
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Homework Statement
Calculate the moment of inertia of a spherical shell (i.e. hollow sphere) of uniform surface density about an axis passing through its center.
Homework Equations
The Attempt at a Solution
Integral ( r^2 * dm)
Integral (r^2 * p * dV) ... where p=density
p * Integral (r^2 * dV)
where V= (4/3)* pi * r^3
and dV= 4 * pi* r^2
therefore,
p * Integral (r^2 *4 * pi* r^2)
4*p*pi* Integral (r^4)
4*p*pi* ((r^5)/5) from 0 to r
p=density=m/V= m/(4/3 * pi * r^3)
4*m/(4/3 * pi * r^3)*pi* ((r^5)/5
(3*m*r^2)/5
but it should be (2*m*r^2)/3.
Please help!