Pulley Revolutions

Question:

SORRY MY ENGLISH. I"M SENDING YOU THIS QUESTION FOR HAVING AN AUTHORITY ANSWER FOR A PRACTICE MATTER. IF I HAVE A SYSTEM CONSISTENT THREE PULLEYS : A,B AND C, AND FOR A AND B EXISTS THE SAME RATIO OR DIAMETER DIMENSIONS, I THINK THEY"LL TAKE THE SAME NUMBER OF ROUNDS CONECTED BY A BAND. BUT IN THE SYSTEM, C PULLEY HAS A DIAMETER ABOUT HALF OF A OR B. DOES C TAKES THE SAME NUMBER OF ROUNDS THAN A OR B PULLEYS? DOES EXISTS SOME PROPORCIONAL KEY TO KNOW HOW MANY ROUNDS ITS TAKE? NOTE THAT THE THREE PULLEYS ARE IN A SAME SYSTEM CONECTED BY A BAND. SINCERELY THANKS,

Answer:

Your English is superior to my Spanish. My understanding of your question is that you have a system of three pulleys with a single band passing over all three. Assuming that the band does not stretch and does not slip on any of the pulleys, the velocity of the surface where the band contacts each pulley will be the same. The angular velocity of a disk is the tangential velocity divided by the radius so a half size pulley will turn twice as fast as a full sized one.