- #1

- 53

- 1

## Main Question or Discussion Point

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 = MR

m/M = pi*r

m = M*r

I = MR

I = MR

I = M/2R

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 = MR

^{2}/2 - mr^{2}/2m/M = pi*r

^{2}*h/pi*R^{2}*h = r^{2}/R^{2}m = M*r

^{2}/R^{2}I = MR

^{2}/2 - M*r^{4}/2R^{2}I = MR

^{4}/2R^{2}- M*r^{4}/2R^{2}I = M/2R

^{2}*(R^{4}- r^{4})