If gear A has 30 teeth and rotates at 30 rpm, how fast will gear B, which has 15 teeth, rotate when driven by gear A?

To determine how fast gear B rotates when driven by gear A, it's essential to understand the relationship between the number of teeth on the gears and their rotational speeds. The principle governing this relationship states that the speed of rotation is inversely proportional to the number of teeth. This means that as the number of teeth decreases, the rotational speed increases, assuming one gear is driving the other.

In this scenario, gear A has 30 teeth and rotates at 30 revolutions per minute (rpm). Gear B, which has 15 teeth, is meshed with gear A. Since the two gears are interconnected, when gear A completes one full revolution, it causes gear B to complete a number of revolutions that can be calculated using the following formula:

Speed of gear B = (Number of teeth on gear A / Number of teeth on gear B) × Speed of gear A

Substituting the given values:

Speed of gear B = (30 teeth / 15 teeth) × 30 rpm Speed of gear B = 2 × 30 rpm Speed of gear B = 60 rpm

Therefore, gear B rotates at 60 rpm when driven by gear A. This relationship between the gears reveals how the differing number of teeth affects their