PULLEY SYSTEMS  VELOCITY RATIO  1
V. Ryan © 2010
PDF FILE  CLICK HERE FOR PRINTABLE WORKSHEET  
The diagram opposite shows a small driver pulley pulling round a larger driven pulley. The rpm (revolutions per minute) of the larger driven pulley wheel will be less than the smaller driver pulley wheel. The same principle regarding speed of rotation regarding gears applies to pulley systems as well. 





WORKING OUT THE VELOCITY RATIO OF PULLEYS 



The system shown above has a driver pulley attached to a motor. When the motor is switched on the driver pulley revolves at 20 rpm. The diameter of the driver pulley wheel is 200mm and the driven pulley wheel is 400mm. This means for every single revolution of the larger driven pulley wheel, the smaller driver pulley wheel rotates twice. This is due to velocity ratio. The ratio can be worked out mathematically in different ways. The two most likely methods are shown below 

PLEASE NOTE  WHEN WORKING OUT VELOCITY RATIO  THE
NUMBERS ARE ARRANGED IN THE SAME ORDER OF THE PULLEYS  IN THIS EXAMPLE
THE DRIVER COMES FIRST, FOLLOWED BY THE DRIVEN IN AN EXAM YOU MAY BE ASKED TO PUT THE DRIVER OR DRIVEN NUMBER FIRST. 

An alternative method is to call the ‘DISTANCE MOVED’ as simply being DIAMETER. This makes the calculation easier to understand, although using this terminology may not be accepted in an examination.  
This means that the larger pulley wheel (the driven pulley wheel) revolves half as fast compared to the smaller driver pulley wheel. In effect the driven pulley wheel is slower and revolves half as many times as the driver. This means if the rpm of the driver pulley wheel is divided by 2, the output rpm of the driven pulley wheel will be found. 



