A horizontal plane supports a stationary vertical cylinder of radius \(R\) and a disc \(A\) attached to the cylinder by a horizontal thread \(AB\) of length \(L\) (see figure above, top view). An initial velocity \(v\) is imparted to the disc, as shown above. How long will it move along the plane until it strikes against the cylinder?

**Details and Assumptions:**

- Neglect friction at all contact surfaces.
- Do not consider gravitational forces.
- The radius of the disc as compared to the radius of the cylinder is very small.

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