When a gear rotates 20 revolutions, it achieves an angular velocity of 30 rad/s, starting from rest. determine its constant angular acceleration in units of rad/s2?

Initial angular velocity = 0 (starting from rest)

Final angular velocity = 30 rad/s

Distance traveled = (20 rev) * (2π rad/rev) = 40π rad

Let the angular acceleration be α rad/s².

Then

(30 rad/s) ² = (0 rad/s) ² + 2 * (α rad/s²) * (40π rad)

α = 3.58 rad/s²

Answer: 3.58 rad/s² (nearest hundredth)