Final answer:
Increasing the diameter of the pinion in a rack and pinion system causes the rack to move a longer distance per rotation, due to the increased circumference of the pinion.
Step-by-step explanation:
If the diameter of a pinion is increased in a rack and pinion system, the rack would move a longer distance for each rotation of the pinion. This is because the circumference of the pinion, which directly engages with the rack, would be greater, leading to a larger movement of the rack per revolution. The relationship between the force applied and the distance traveled in circular motion systems is somewhat analogous to other mechanical systems, such as levers and pendulums, where the length of the lever arm or pendulum affects the torque or the rate of swing respectively.