Question

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?

Answer 1

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)