Two thin rigid slabs with mass $m_1$ and $m_2$ perform a plane motion. Slab $1$ is rotatably fixed in the orgin $O$ and linked with the second slab on its end. At time instant $t_0,$ the system is let loose and moves in the gravitational field $g.$

Evaluate the translational part of the kinetic energy for the slab $2,T_{S,l_2},$ with respect to its center of mass. $(6$ points$)$

Evaluate the rotational part of the kinetic energy of both slab, $T_{\text{r}\text{o}\text{t},l_1}$ and $T_{\text{r}\text{o}\text{t},l_2},$ with respect to their center of mass as well as the potential energy $$ of the whole system. $(4$ points each$)$

Given: $,=60,=30,m_1=6kg,m_2=7kg,g=10m{s}^{-2},{}^{}=3s^{-1},{}^{}=1s^{-1},l_1=4m,l_2=6,928m.$

$x,A$

Insert the correct solution at an accurracy of four significant numbers into the corresponding fields:

$T_{S,l_2}=,[kg{m}^2{s}^{-2}]$

$T_{\text{r}\text{o}\text{t}{l}_1}=,[kg{m}^2{s}^{-2}]$

$T_{\text{r}\text{o}\text{t}{l}_2}=,[kg{m}^2{s}^{-2}]$

$=,[kg{m}^2{s}^{-2}]$