$6/162$ A planetary gear system is shown, where the gear teeth are omitted from the figure. Each of the three identical planet gears $A,B,$ and $C$ has a mass of $0\mathrm{.}8$ kg $,$ a radius $r=50mm,$ and a radius of gyration of $30$ mm about its center. The spider $E$ has a mass of $1\mathrm{.}2$ kg and a radius of gyration about $O$ of $60$ mm $.$ The ring gear $D$ has a radius $R=150mm$ and is fixed. If a torque $M=5N*m$ is applied to the shaft of the spider at $O,$ determine the initial angular acceleration $$ of the spider.

Problem $6/16$