Question

Find the center of mass of a solid cylinder C that has density f=3z^2, bounded by x^2+y^2<(or equal)1 and 0<(or equal) z <(or equal)1

Answer 1

General definition is :
\(\vec {OG} = \LARGE\frac 1m \Large\iiint \limits_ {P\in Cyl.} \,\normalsize \vec{OP}\;\mathrm{d}m\)

which leads here to :

\(h=\LARGE\frac 1m \Large \int _0^1 \,\normalsize z\;\mathrm{d}m\)

where

\(m= \Large \int _0^1 \,\normalsize \mathrm{d}m\)