Calculate Torque in a Sprocket or Pulley Given Belt or Chain Tension

Understand the relationship between the torque in a sprocket or pulley and the tension that exists in a chain or belt. Regardless of whether we look at the input or output side of a chain or belt drive system, the relationship between torque and force can be viewed in the same way.

The points at which the belt or chain enter or exit the pulley can be viewed as points where the tension force is applied to the pulley; with each tension force producing a competing torque.

Using the Torque Equation we can calculate the Net Torque on the pulley in order to generate an equation that ties the torque together with the forces in the belt or chain.

In the case of a belt, it is friction which serves to transfer tension from the belt into the pulley, which ultimately leads us to the Capstan equation, an important topic for another video.

This problem appears in introductory physics and engineering courses such as AP Physics 1, AP Physics C Mechanics, PLTW POE, and appears on a variety of exams including A Levels and JEE.