Final answer:
An object exiting circular motion will travel in a straight path relative to the Earth (assuming no other forces act upon it), due to the absence of a centripetal force, but will appear to follow a curved path to an observer on the rotating frame due to the fictitious Coriolis force.
Step-by-step explanation:
When something exits uniform circular motion, such as a ball being released from a merry-go-round, it no longer experiences the centripetal force that was keeping it on its circular path. In the absence of this force, and assuming negligible friction, the object will move in a straight line path relative to the Earth according to Newton's first law of motion. This straight-line motion is tangential to the point on the circle where the object was released. However, to an observer on the merry-go-round, the motion appears as a curved path due to the rotating frame of reference. This perceived curvature is attributed to a fictitious force known as the Coriolis force, which is apparent in non-inertial frames of reference but doesn't exist in an inertial frame of reference such as the Earth's surface. Therefore, the ball's actual path is straight but appears curved when viewed from the rotating merry-go-round.
In conclusion, when an object leaves its circular motion, it will move in a straight line unless acted upon by another force. The path only appears curved to observers in a rotating frame of reference due to the Coriolis effect.