Belt speed is related to pulley diameter and rotation rate by which formula?

• A. v = π × D × N
• B. v = 2 × π × D × N / 60
• C. v = π × D × N / 60
• D. v = π × D × N / 120

Answer: (C)

Belt speed is the linear distance the belt travels each second. It comes from the belt advance per pulley turn, which is the circumference of the pulley, π times its diameter. If the pulley makes N revolutions each minute, the belt moves πDN each minute. To convert that to seconds, divide by 60, giving v = (πDN)/60. This form correctly uses the true distance per revolution and the proper time unit. Using 2πD would double the distance per revolution, and dividing by 120 would give half the correct value, so those forms don’t match.