- #1
quietrain
- 655
- 2
Hi, i am trying to find the moment of inertia of a uniform density solid sphere about z-axis
I = integrate => x^2 dm
x = perpendicular distance from z-axis to anywhere in sphere
so by pythagorus theorem, r^2 - z^2 = x^2
since dm = p dV
and V = 4/3 (//pi)r^3
dV = 4(//pi)r^2 dr
so I = integrate=> r^2 - z^2 pdV
but the problem is z is a variable.
so how do i convert z?
assuming i put z = rcos θ,
then i will have a θ variable now.
i tried integrating θ from 0 to (pi) but the answer is wrong, its not 2/5mr^2
so what should i do?
thanks
I = integrate => x^2 dm
x = perpendicular distance from z-axis to anywhere in sphere
so by pythagorus theorem, r^2 - z^2 = x^2
since dm = p dV
and V = 4/3 (//pi)r^3
dV = 4(//pi)r^2 dr
so I = integrate=> r^2 - z^2 pdV
but the problem is z is a variable.
so how do i convert z?
assuming i put z = rcos θ,
then i will have a θ variable now.
i tried integrating θ from 0 to (pi) but the answer is wrong, its not 2/5mr^2
so what should i do?
thanks