- #1
jordanl122
- 14
- 0
I need to derive the moment of inertia for a solid sphere, but I'm having some trouble.
I did the following.
I=?r^2dm
given density, p= m/V
pV=m
so pdV=dm
and differentiating V wrt r, d(4/3?r^3)dr = 4?r^2
so p4?r^2dr=dm and plugging that in I get
I=?r^2(p4?r^2)dr
I pull the p4? out in front
I=p4??r^4dr
evaluating the integral I get
I=(M/(4/3?r^3))4?(r^5/5)
simplifying the terms I get
I=3/5mr^2
which is a universe off from what the answer should be, if anyone can show me where I went wrong I would be very appreciative. Thanks.
I did the following.
I=?r^2dm
given density, p= m/V
pV=m
so pdV=dm
and differentiating V wrt r, d(4/3?r^3)dr = 4?r^2
so p4?r^2dr=dm and plugging that in I get
I=?r^2(p4?r^2)dr
I pull the p4? out in front
I=p4??r^4dr
evaluating the integral I get
I=(M/(4/3?r^3))4?(r^5/5)
simplifying the terms I get
I=3/5mr^2
which is a universe off from what the answer should be, if anyone can show me where I went wrong I would be very appreciative. Thanks.