A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.705 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the merry-go-round one third of a revolution in front of him (which means the dog has to move for additional 2/3Pi angular displacement before reaching the bone.) At the instant the dog sees the bone (t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.0135 rad/s2. At what time will the dog reach the bone?
Hint: use rotational kinematics equations for both, dog and the merry-go-round and set them equal to each other - this means the dog has reached the bone. Then solve it for time, t.