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Problem $12\mathrm{.}069-$ A block sliding inside a slot

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A $0\mathrm{.}5-$kg block B slides without friction inside a slot cut in arm OA which rotates in a vertical plane. The rod has a constant angular acceleration $\backslash$theta $=10$ rad$/$s$2$

$.$ Know that when $\backslash$theta $=66$

and r$=0\mathrm{.}8$ m

$,$ the velocity of the block is zero.

An illustration of a small block inside the slot of a vertical arm that is inclined toward southeast.An illustration. A vertical arm labeled O A is fixed to a horizontal hinge support on the left, at the the top end O$.$ A slot is cut in the arm from a point close to A till a point to the left of the center. A small block labeled B is inside the slot at a point to the right of the center. The vertical arm is inclined toward southeast at angle theta from the vertical. The slant height from the center of the hinged support O to the center of the block in the slot is labeled r$.$

Problem $12\mathrm{.}069.$c $-$ Relative acceleration of the block

Determine the relative acceleration of the block with respect to the arm at this instant. $($Round the final answer to three decimal places.$)$

The relative acceleration of the block with respect to the arm is

m$/$s$2$

$.$