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Let's say we have two rotating disks and one disk is given some angular velocity. As one disk rotates, due to friction the other disk should rotate as well. The two disks are completely identical (radii, mass etc). The two disks are lined up next to each other horizontally, and only the rims of the two disks are in contact.

In this setup, the normal force and the frictional force are the most important forces. But what is the exact relation between the forces and how can we calculate them?

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    $\begingroup$ Depends on a whole load of things (e.g. material of the discs), but a common relationship between tangential frictional force and normal force is $F_{max} = \mu N$ where $N$ is the normal reaction force and $\mu$ is some coefficient of friction. That said, the frictional force cannot exceed that needed to rotationally accelerate the disc. $\endgroup$ May 31, 2021 at 11:12
  • $\begingroup$ @jumbot What exactly do you mean "the frictional force [,,,] needed to rotationally accelerate the disc"? For any force, there will be a corresponding acceleration given by $ FR/I$ where R is radius if disc, and I is moment of inertia. Where does the limit come here? Also, since the discs have relative motion, wouldn't the coefficient of friction necessarily be the coefficient of kinetic friction? $\endgroup$
    – Manish S
    May 31, 2021 at 13:19

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Initially, there is a relative motion between the two discs. So, the frictional force is given by $ F_{fr} = \mu_k N $, where $N$ is the normal force, and $\mu_k$ is the coefficient of kinetic friction. At one point, the relative velocity between the two discs becomes 0. At this stage, the frictional force also be 0.

Hope this answers your question.

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