Final answer:
In a gear system with an idler gear placed between a driving and a driven gear, the driven gear rotates in the same direction as the driving gear. The idler gear's role is simply to transfer motion, not to alter the direction of the rotation.
Step-by-step explanation:
When an idler gear is placed between the driving and driven gear, the function of the idler gear is to transmit rotation from the driving gear to the driven gear without altering the direction of rotation. Hence, if the driving gear is rotating clockwise, the idler gear would rotate counterclockwise, and this would make the driven gear rotate clockwise, in the same direction as the driving gear.
Gear systems are fundamental in physics, particularly in the study of rotational motion and mechanical advantage. When two gears are meshed together directly, they rotate in opposite directions. This implies that if gear A, for example, turns clockwise, the directly meshed gear B would turn counterclockwise. However, with an idler gear (Gear C) between A and B, gear A would turn Gear C counterclockwise, which in turn would rotate Gear B clockwise, matching the rotation direction of Gear A.
Therefore, when an idler gear is placed between the driving and the driven gear, the driven gear rotates in the same direction as the driving gear. This holds regardless of the number of teeth on the idler gear since its primary purpose is to change the direction of rotation while transferring the motion.