$($a$)$

$\_($B$)$

$($b$)$

A spin$-$stabilized spacecraft far from any other massive object initially rotates with vec$(\backslash$omega $)\_(1)=-57$kra$($d$)/($s$)$ as it

translates along the z$-$axis. As shown in figure $($a$),$ the spacecraft consists of a rigid $212-$kg cylinder$-$shaped

center module with $($k$\_($G$))\_($z$)=0\mathrm{.}9$m whose center of mass G lies along the z$-$axis and two $3\mathrm{.}8-$kg small weights

A and B that initially are fixed to the outer surface of the center module $($r$=1\mathrm{.}99$m$).$ In order to reduce the

rotation rate, A and B are released on wires of negligible mass as shown in figure $($b$),$ where l$=29$m$.$

Find the magnitude of the spacecraft's resulting angular velocity, $\backslash$omega $\_(2).$ Neglect the size of A and B$.$

CORRECT ANSWER: $\backslash$omega $2=1\mathrm{.}53984175715($rad$)/($s$).$

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