$6$ points$)$ Due to motor $M,$ the small gear $S$ experiences an angular velocity given by:

${}_S()=(9\mathrm{.}2{}^{0\mathrm{.}7})ra\frac{d}{s}$

where $$ is the angular displacement of gear $S$ measured in radians. What is the magnitude of the angular acceleration of the large gear $D$ at the moment the small gear $S$ has rotated $6\mathrm{.}4$ times around. For clarity, the radii given in the figure are: $r_S=60mm,r_D=150mm.$