In the calculation of shaft speed and shaft torques of a belt drive system, which of the following applies?

• A. Shaft speeds are inversely proportional to pitch diameters
• B. Shaft speeds are proportional to pitch diameters
• C. Torques are proportional to belt width
• D. Power is inversely proportional to belt tension

Answer: (A)

In a belt drive, the belt moves at the same linear speed on both pulleys. The belt speed relates to each pulley by v = π D N / 60, where D is the pitch diameter and N is the shaft speed in rpm. Because the belt speed is the same for both pulleys, D1 N1 = D2 N2, which means the shaft speeds vary inversely with the pulleys’ pitch diameters: if one pulley is larger, the corresponding shaft turns more slowly. This inverse relationship is why shaft speeds are proportional to the inverse of the pitch diameters.

The other ideas don’t fit because increasing the pitch diameter while keeping belt speed constant would force a lower shaft speed, not a higher one. Torque depends on belt tension and the radius at which the belt applies force, and while belt width affects how much tension can be carried, it isn’t a simple direct proportional factor for torque. Power depends on both torque and speed, not inversely on belt tension.