A jeweler's grinding wheel slows down at a constant rate from 185 rad/s to 105 rad/s while it rotates through 16.0 revolutions. How much time does this take?

  t = 0.6933 s

Explanation:

This is a rotational kinematics exercise, let's find the angular acceleration of the wheel

          w² = w₀² + 2 α θ

          α = (w² - w₀²) / 2 θ

Let's reduce the angles to the SI system

         θ  = 16 rev (2π rad / 1 rev) = 32π rad

let's calculate

          α = (105² - 185²) / (2 32π)

          α = -115.39 rad / s²

now let's use the relation

           w = w₀ + α t

           t = (w- w₀) /α

           t = (105 - 185) / (- 115.39)

           t = 0.6933 s