Calculate Torque Transfer Between Rotating Friction Discs

This problem is a classic example of how to apply physical principles of friction, force and pressure as well as basic integration into physics.
Friction producing a torque, rather than acting at a single radius, is applied across the face of an entire rotating disc. As a result we have to set up a function for the torque at a single radius, then integrate that function across the entire face of the disc.
This problem comes up in calculus based physics courses as well as mechanics courses.

[@jonathanwilliam1269]

Best explanation I've ever seen, so cleverly simple didatic

[@INTEGRALPHYSICS]

Glad you think so!

[@mr2.0facts84]

What an absolute tremendous explaination

[@JackTriceAero]

@INTERGALPHYSICS how is the equation change when you have a pin on disc scenario?

[@towdinghuei5198]

Hi, may I know whats the different of the FN (first equation) and F (last equation)? I have gone through your video several times but still not understand. Thank you in advance.

[@INTEGRALPHYSICS]

FN is the same as the total clamping force F.

[@towdinghuei5198]

@@INTEGRALPHYSICS Thank you for the clarification!

[@emcv1880]

Clear deviation, but the COF dropped in the last equations. Might have some influence on the final torque.

[@INTEGRALPHYSICS]

Cof moved next to the 'F' in the line before I set up the integral.

[@vijaymerni]

How can be radial friction force calculate instead of Torque?

[@INTEGRALPHYSICS]

Sorry, I'm not sure I understand the question. The friction does not act radially, it acts tangentially.

[@sgtbilko2950]

So a clutch then?

[@INTEGRALPHYSICS]

Yup.