In a rotating cylindrical space colony of radius \(R\) and angular velocity \(\omega\) about its axis of rotation, a ball of mass \(m\) is thrown with speed \(v=\omega R / 2\) ) from a point halfway between the rotation axis and rim, in a direction exactly opposite to the rotation direction, as seen by colonists.

(a) State the nature of its subsequent path in the inertial frame in which the cylinder is seen to rotate.

(b) Sketch the ball's path in the rotating frame of the colony, and show that this path is predicted by the pseudoforces acting upon it.