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 1/8^th 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?