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.

[@CyborgVampireBell]

I wish you were my teacher, I could have learned this! My life would have been different.

[@abuzuhair9945]

Please elaborate a bit on direction of friction on belt and pulley

[@INTEGRALPHYSICS]

In the absence of friction the belt would just slide over the output pulley. It is friction that 'transfers' force (or really energy) from the belt to the pulley. By it's very nature friction will always resist the relative motion between two objects, meaning it will act tangentially on the pulley to move the pulley in the direction the belt is moving, and in turn (3rd Law) it will act against the motion of the belt.

[@atila8623]

Nice

[@vorapobautomation9760]

How to calculate the speed in MPM. of web wider and unwinder machine if the empty roll diameter = 0.934 m. and the web thickness is 1mm. ?

[@rationallyjustified]

im trying to calculate the amount of HP an AC motor requires with any 2 pulleys (1 attached directly to the motor) the other attached with a rope that would go to another series of 4 pulleys with 40 lbs. (less pulleys could be used) my idea is to basically use old drilling techniques to make a power hammer for blacksmithing, i saw old mining rights with a slack rope to and it inspired this contraption. sorry i'm ignorant when it comes to math. any ideas?

[@AbrahamMorrisNoahjrTv]

Sure

[@shooter7a]

kind of a crock....you did not even solve an example...