Question

On the topic of thermal physics:

two plane discs, each of radius 5 cm, are mounted coaxially with their adjacent surfaces 1 mm apart. They are in a chamber containing Ar gas at viscosity = 2.1*10^-5 and are free to rotate about their common axis. One of them rotates with angular velocity 10 rad/s. find the torque that must be applied to the other to keep it stationary

Answer 1

. Relevant equations I know there's an also right equation of

F/A = viscosity*d/dz

Where is the average x-velocity at a given z (z is along the axis).

The attempt at a solution I tried taking ux to be the component of a particle's velocity along the theta direction (perpendicular to the radius of the disc), and replacing it with rw. I then tried to integrate that equation up there wrt z, so that the RHS gives viscosity*r*(w - w0) where w0 is the value given for angular velocity and w is the value at the other disc. However I am confused as to what F is. I think it's the force exerted on the spinning disc, but if so how do I know what it is? I thought about using Idw0/dt = torque, but w0 is constant. I also thought about centripetal force acting on parts of the disc, but I don't understand how that could be right