A bobbin of thread is pulled by a sewing machine. The bobbin is made of plastic with a thickness of $1$ mm with dimensions shown below. The machine pulls with a force $F_{\text{p}\text{u}\text{l}\text{l}}=1\mathrm{.}2N$

a$)$ Draw a FBD for the bobbin $($show both side and top views$)$

b$)$ write out $vec(F)$ and $vec()$ for the bobbin

c$)$ Write out the formula $($do not need to numerically evaluate$)$ for the Moment of Inertia of the bobbin assuming the bobbin is constructed of shells and rods