Final answer:
Gear ratio expresses the ratio of the number of teeth on two gears. In hydraulic systems and transformers, the area ratio and coil ratio respectively determine force amplification and voltage increase. Angular velocity of meshed gears changes in an inverse relationship to changes in applied force and torque.
Step-by-step explanation:
The gear ratio is a dimensionless figure which expresses the ratio of the number of teeth on one gear (output gear) to the number of teeth on another gear (input gear). For example, if there are 3 teeth on the input gear for every 1 tooth on the output gear, the gear ratio is 3:1. This would make the output gear turn three times slower than the input gear but would increase the torque threefold. Similarly, in a hydraulic system designed to increase force, the ratio of areas or diameters of cylinders determines the multiplication of force according to Pascal's principle. Moreover, in a step-up transformer, the ratio of the number of output coils to input coils determines the increase in voltage, so if the voltage is increased fivefold, the ratio of coils must also be increased fivefold. Finally, the angular velocity of two meshed gears will change in magnitude inversely; if more force increases the torque on one gear, the other gear's angular velocity will change correspondingly.