60Velocity Shear
The rotor moves at 14000 meters per second. The track moves at 0 meters per second. They are separated by 1cm of vacuum, with spacing actively controlled by a magnetic field. Sounds like a formula for disaster, right?
One way to characterize the small spacing versus high velocity problem is as a ratio of these two numbers, space/velocity. For the launch loop, this is 1cm/14000m/s or 720 nanoseconds. That seems like a tiny number.
However, the platter of a 3.5 inch hard drive is moving at 14 meters per second, and the spacing between the head and the platter is 10 nanometers. A running hard drive can be subjected to many gees due to unpredictable impact forces, or unexpected power removal. 10nm divided by 14m/s is 720 picoseconds, a thousand times smaller. The head spacing on a hard drive is maintained by airflow, this is called a "flying head". However, there is no other active control, beyond the servo that moves the head laterally across the surface, and removes it very rapidly when the disk shuts down. If power is removed unexpectedly, the energy stored in the spinning platter is used to write buffered data, then move the head to a safe track. A disk drive manages all of this for years of operation without breaking the very fragile head or magnetic platter surface.
In reality, the problem is NOT relative velocities, it is relative energies. The issue in a launch loop is hypervelocity spalling cascades. A sufficiently large particle either rotor or track at 14000 meters per second will have enough energy to kick loose more mass, which may impact the opposing surface and kick loose more.
This is potentially problematic over a range of particle sizes. At the smallest, atoms will strike the side, and trigger spalling. This problem can probably be dealt with by boron plating the interior components, boron tends to absorb atoms below a certain number of electron volts of energy.
At larger sizes, dust will strike the side and vapourise/turn into plasma. This plasma will take up volume and will press on the rotor. However, the high speed is on our side here, the total mass of rotor that will be pressed is large, both because it's moving and because it's multiple kilograms per metre, and hence it will move little and the plasma shoulld eventually be taken out by the vacuum system.
At the gram-sizes it's more iffy, particularly on the turnaround sections which are high g. If you're lucky the fragment will skim along on a layer of plasma until it slows or evaporates. The worse case would be if it ran headlong into an obstruction and explodes the sheath.