Calculate the internal forces in members using the proper sign conventions

Draw shear and moment diagrams for beams $($and other simple structures$)$

Calculate the centroid of a line, area, and volume using both integration and composite bodies

An instrument for measuring the direction of wind is shown. It consists of a hemispherical aluminum cap, cylindrical plastic body, and a triangular sheet metal fin. The instrument is symmetrical about the xy plane, and the aluminum, plastic, and sheet metal have specific weights of ${}_{al}=0\mathrm{.}1l\frac{b}{i}{n}^3,{}_{pl}=0\mathrm{.}04l\frac{b}{i}{n}^3,$ and ${}_{sm}=0\mathrm{.}09l\frac{b}{i}{n}^3,$ respectively. The thickness of the sheet metal fin is $0\mathrm{.}25$ inches. Calculate the $x,y,$ and $z$ position of the center of gravity $($Note that this will be different than the centroid because the densities are different$).$