Irodov Solution 1.89

At any radius r the maximum providable force of friction is given by mgk. With respect to a stationary observer, the rotating cycle is subject to a centripetal acceleration of directed towards the center of the circle (in the rotating frame of the cycle this will be felt as the centrifugal force acting radially outwards) . Thus, at any radius the at the maximum sustainable velocity v we have,



Now the radius corresponding to the maximum sustainable velocity can be determined by maximizing the square of the expression for the square of the velocity as well and making sure that its second derivative is -ive.











At r=R/2 thus, the cyclist can maintain the maximum possible velocity without slipping and its value can be determined by substituting in the expression for velocity determined above as .