$2.$ Consider the "Comprehensive Example" in the slides $("$Rigid Body$\_$L$11").$ Using the numbers given in L$11$ answer the following questions:

a$)$ Find the mass center of the system, relative to the $\backslash ($ b$^\{\backslash$prime$\}\backslash )\text{'}$ frame. Give your answer as a Gibbs vector expressed in the b$\text{'}$ frame. $(10\backslash \%)$

b$)$ Find the inertia matrix of the system, about the mass center of the cylinder, and relative to the b$\text{'}$ frame. $(10\backslash \%)$

c$)$ Find the inertia matrix of the system about the mass center of the composite body and relative to the b$\text{'}$ frame. $(10\backslash \%)$

d$)$ Find the principal axes and principal moments of inertia of the composite body. You may find the Matlab function $\backslash ([\backslash$mathrm$\{$V$\},\backslash$mathrm$\{$D$\}]=\backslash$operatorname$\{$eig$\}(\backslash$mathrm$\{$I$\})\backslash )$ useful in solving this problem. $\backslash ((10\backslash \%)\backslash )$