Gears $A,B,C,$ and $D$ have radii of $15mm,55mm,25$ mm $,$ and $70$ mm $,$ respectively $($Figure $1)$

If gear A rotates with an angular velocity of ${}_A=(B_A+1)ra\frac{d}{s},$ where $B_A$ is the angular displacement of gear $A_A,$ measured in radians, determine the angular acceleration of gear $D$ when $8_A=5$ rad, starting from rest.

Express your answer to three significant figures and include the appropriate units.

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