Answer
$\frac{\omega_o}{\omega_i}=0.517$
Work Step by Step
Body
$m=52kg$
$r=0.15m$
$I_B=\frac{MR^2}{2}=\frac{(52kg)(0.15m)^2}{2}=0.585\frac{kgm^2}{2}$
Arms outstretched
$m=4kg$
$l=0.60m$
$I_A=\frac{Ml^2}{3}=\frac{(4kg)(0.60m)^2}{3}=0.72\frac{kgm^2}{2}$
Arms in
$m=60kg$
$r=0.18m$
$I_{in}=\frac{MR^2}{2}=\frac{(60kg)(0.15m)^2}{2}=0.675\frac{kgm^2}{2}$
$I_{out}=0.585\frac{kgm^2}{2}+0.72\frac{kgm^2}{2}=1.305\frac{kgm^2}{2}$
$L_o=L_i$
$I_o\omega_o=I_i\omega_i$
$\frac{\omega_o}{\omega_i}=\frac{I_i}{I_o}=\frac{0.675\frac{kgm^2}{2}}{1.305\frac{kgm^2}{2}}=0.517$
