Motorcycle circle ***
A motorcyclist wishes to travel in a circle of radius R on level ground. The coefficient of friction between the tires and the ground is μ. The motorcycle starts at rest. What is the minimum distance it must travel in order to achieve its maximum allowable speed, that is, the speed above which it will skid out of the circular path? Solve this in two ways:
((a)) Write down the radial and tangential F=ma equations (you'll want to write a as vdv/dx), and then demand that the magnitude of the friction force equals μmg in the optimal case. Take it from there.
((b)) Let the friction force make an angle β(t) with respect to the tangential direction. Write down the radial and tangential F=ma equations (you'll want to write a as dv/dt), and then take the derivative of the radial equation. Take it from there (this is the slick way).