Final answer:
Gear #4 will turn counterclockwise as the direction of rotation alternates with each gear in a series. The increased force applied to gear A causes the angular velocity of gear B to increase in magnitude.
Step-by-step explanation:
When four gears are connected in a series, the direction of rotation alternates with each gear due to the interlocking of their teeth. If Gear #1 turns clockwise, then Gear #2 will turn counterclockwise, Gear #3 will rotate clockwise again, and finally, Gear #4 will turn counterclockwise.
The relative speed of the gears (without additional information) depends on their size (number of teeth) and the input torque, but in this scenario, only the direction is considered, so the answer is that Gear #4 will turn counterclockwise. If we consider the situation where gear A meshes with gear B and more force is applied to gear A, creating more torque, the angular velocity of gear B would increase in magnitude as it responds to the increased force exerted by gear A.