Question $6$

$($#$710921)\{$Multi$-$concept$\}$

A tabletop micro$-$centrifuge spins at $6000$ rpm $($revolutions per minute$).$ When the lid is opened, the automatic shut$-$off circuit kicks in and the micro$-$centrifuge begins to slow down with a constant angular deceleration. In the first $10\mathrm{.}0$ seconds immediately after the shut$-$off, it the micro$-$centrifuge completes $686$ full revolutions. Calculate the angular acceleration rate of the slowing micro$-$centrifuge in units of rad$/$s ${?}^2.($Report your answer as a negative number to reflect the fact that the device is actually decelerating$)$

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Please enter a numerical answer below. Accepted formats are numbers or $"$e$"$ based scientific notation e$.$g$.0\mathrm{.}23,-2,1$e$6,5\mathrm{.}23$e$-8$

Enter answer here

$-45\mathrm{.}8$

$ra\frac{d}{s^2}$