Firefighter Practice Exam

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If pulley A has a circumference of 14.75 inches and pulley B has a circumference of 23.25 inches, how fast will pulley A turn if pulley B is at 200 rpm?

315.25 rpm
274.67 rpm
192.83 rpm
126.88 rpm

The correct answer is: 315.25 rpm

To understand how fast pulley A will turn when pulley B is at 200 revolutions per minute (rpm), we need to consider the relationship between the circumferences of the two pulleys. The speed of a pulley in a belt system is inversely proportional to its circumference. This means that if one pulley is larger (has a greater circumference), it will turn slower compared to a smaller pulley, assuming they are connected by a belt without slip. First, we need to calculate the ratio of the circumferences of pulley B to pulley A: 1. Circumference of pulley A = 14.75 inches 2. Circumference of pulley B = 23.25 inches To find the ratio: Ratio = Circumference of B / Circumference of A Ratio = 23.25 / 14.75 = 1.577 This ratio indicates how many times pulley B's circumference fits into pulley A's. Since pulley B is moving at 200 rpm, we can find the speed of pulley A by multiplying the rpm of B by the ratio we calculated: Speed of pulley A = Speed of pulley B * Ratio Speed of pulley A = 200 rpm * 1.577