Kinetics of body

When the disk rotates and slides at the same time, a relative motion exists between the point of the disk which is in contact with the ground and the ground itself and the force of friction has the magnitude , where is the coefficient of kinetic friction. In this case, however, the motion of the mass center G of the disk and the rotation of the disk about G are independent, and the acceleration of the center is not equal to the product of angular acceleration and radius.

The three different cases are summarized as follows:

      Rolling, no sliding                                        

      Rolling, sliding impending                             

      Rolling, and sliding                                     a and independent.

When it is not known whether or not a disk slides, it should first be assumed that the disk rolls without sliding. If F is found smaller than, or equal to, , the assumption is proved correct. If F is found larger than , the assumption is incorrect and the problem should be started again, assuming rolling and sliding.

Now, let us solve a problem on rolling.