$7\mathrm{.}18.$ The three$-$node triangular axisymmetric element shown is rotating with constant angular velocity $\backslash (\backslash$omega $\backslash )$ rads$/$s about the $\backslash ($ z $\backslash )-$axis. Determine the $\backslash (6\backslash$times $1\backslash )$ element load vector $\backslash (\backslash$mathbf$\{$f$\}\backslash )$ due to the resulting body force. Give the answer in terms of $\backslash (\backslash$omega $\backslash )$ and material density $\backslash (\backslash$rho $\backslash ).$