A horizontal turntable at an industrial plant is continuously fed parts
into a slot (shown on the left). It then drops these parts into a basket
(shown on the right). The turntable rotates 180° between these two
stages. The turntable briefly stops at each 1/8th of a turn in order to receive a new part into the slot on the left.
If the rotational speed of the turntable is w radians/second, and the outer radius of the turntable is R2, what must be the inner radius R1 so that the parts fall out of the slot and into the basket, as shown?