Consider a spherical spacecraft with a mass model $($figure; not to scale$)$ consisting of a sphere of

diameter $d_0=5\mathrm{.}2ft$ and two cylinders with $($cylinder $1)$ the length $h_1=0\mathrm{.}8m$ and diameter

$d_1=1\mathrm{.}3m$ and $($cylinder $2)$ the length $h_2=2\mathrm{.}4m$ and diameter $d_2=0\mathrm{.}8m.$ The mass is

distributed uniformly in the sphere and in the cylinders, but the average sphere density ${}_S$ is

smaller than the density of the cylinders ${}_C,$ such that ${}_C=1\mathrm{.}6{}_S.$ Total mass of the

view from top

spacecraft is $M_{SC}=2800kg.$

Two thrusters symmetrically$-$located at the sides of cylinder $2$ are used to spin the spacecraft up

about the $Z$ axis to a nominal spin rate of ${}_0=36rpm($revolutions per minute$).$ The thrusters

point perpendicular to the axis of cylinder $2$ in the plane $(x,Y),$ as shown in the figure, and provide

thrust $F_0=2\mathrm{.}5lbf$ each. Assume that the mass of the consumed propellant is much smaller than

the mass of spacecraft.

A$.$ Calculate the spacecraft moment of inertia about the axis $Z.($Use appropriate equations shown in

Fig. $11-39,$ p$.482,$ from the LW textbook shown on the next page$)$

B$.$ Calculate the angular acceleration, ${}_0,$ of the spacecraft while spinning up $($give the answer in

$ra\frac{d}{se{c}^2}$ and deg $(\frac{\text{:}}{se{c}^2}\}.$

Problem $16-$ continued on the next page