A wheel of radius r and mass M is rolling (i.e. no slip between the wheel and the surface) on a circular surface of radius R (> > r) as shown in Figure below. Calculate the following quantities (Hint: the condition for the wheel keeps rolling without falling is the centrifugal force is no less than gravity): a) The minimum angular velocity of the wheel when it reaches the bottom point B if it does not detach from the surface when it reaches the top point A (i.e., keeps rolling without falling). b) The velocity and acceleration of the wheel?s mass center e at the instant when it reaches the bottom point B of the circular surface, under the condition of a). c) The angular velocity and angular acceleration of the wheel at the instant when it reaches the top point A of the circular surface, under the condition of a). d) The respective kinetic energies of the wheel when it reaches the bottom and top points of the circular surface.
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