A reel of thread whose rim and spindle are of radius a and b respectively rest of a rough horizontal table. The loose end of the thread passes under the spindle and leads off at an angle α above the horizontal α < 1/2π. Show that the least tension in it will, in general, the wind or unwind the thread according to as α is less or greater than a certain value. When α has this critical value, show that there will be no motion unless the tension exceeds another critical value.