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## Homework Statement

A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a constant force ##F## uniformly distributed across the wheel's face. There is friction between the wheels.

What is the final angular velocity of the two wheels ##\omega_{f}## and how long does it take for the wheels to reach that speed?

## Homework Equations

##\tau=I\ddot{\omega}##, maybe conservation laws?

## The Attempt at a Solution

There is no conservation of angular momentum since the torque is changing.

The initial torque is ##\tau=\frac{2}{3}R_{1}F\mu##. I have to find ##I## for the cylinders. How do I relate ##\tau## at a given time with ##\omega##?