A stick rests on a circle of radius \(R\). The stick makes an angle \(\theta\) with the horizontal and is tangent to the circle at its upper end. Calculate \(\theta\) for which stick is most likely to slip on ground. Enter answer as \(\lfloor 100\theta\rfloor\) where \(\theta\) is in degrees.
Details and Assumptions
Friction exists at all points of contact.
Assume that stick is large enough to keep the system at rest.