What is the formula for calculating the speed of a pulley system?

The formula for calculating the speed of a pulley system is based on the relationship between the rotational speeds (RPM) and the diameters of the pulleys. The correct formula indicates that the product of the RPM and the diameter of one pulley equals the product of the RPM and diameter of another pulley. This formula stems from the fact that the linear speed of the edges of the pulleys must be constant, as they are connected by a belt or cable.

When you multiply the RPM of a pulley by its diameter, you are calculating the linear speed at the rim of the pulley. Since the two pulleys are connected in the system, the linear speeds must be equal. Therefore, the equation balances this relationship by aligning the products for both pulleys. This principle is essential for determining the functioning and compatibility of different pulley sizes and speeds within a mechanical system.

In contrast, the other provided options do not accurately reflect the physical relationship between the pulleys. Some may confuse the proportional relationship, misrepresenting how RPM and diameter interact. The key takeaway is that the correct formula relies on the product of RPM and diameter being equal for each pulley, embodying the essence of mechanical advantage and speed in pulley systems.