- #1
BrainSalad
- 53
- 1
For a uniform, hollow cylinder, why is this derivation wrong?
M = mass of whole solid cylinder
m = mass of missing cylindrical piece
R = radius of whole cylinder
r = radius of missing cylindrical piece
moment of inertia = moment of inertia of whole cylinder - moment of inertia of missing cylindrical piece
I = MR2/2 - mr2/2
m/M = pi*r2*h/pi*R2*h = r2/R2
m = M*r2/R2
I = MR2/2 - M*r4/2R2
I = MR4/2R2 - M*r4/2R2
I = M/2R2*(R4 - r4)
M = mass of whole solid cylinder
m = mass of missing cylindrical piece
R = radius of whole cylinder
r = radius of missing cylindrical piece
moment of inertia = moment of inertia of whole cylinder - moment of inertia of missing cylindrical piece
I = MR2/2 - mr2/2
m/M = pi*r2*h/pi*R2*h = r2/R2
m = M*r2/R2
I = MR2/2 - M*r4/2R2
I = MR4/2R2 - M*r4/2R2
I = M/2R2*(R4 - r4)