Friction - -     Rigid Bodies in Translation and Rotation  (continued)

 

 

                                              

 

 

Next examine case 3  where the disk rolls with slipping in the   ˗ x - direction.

 

          ΣF =  m acx               ˗ Px  + F  + Dx  =  m   aCx                          (1)

 

          ΣF =  m acy =  0         N ˗ mg  + Py  +  Dy  =  0                         (2)  for data  N  =  19 N

 

         ΣMC =  Ic α                  F r  + Dy r  =  (1/2) m r2  α                     (3)

 

And since slipping occurs    F  =  Fmax  =  μ N  =  4.75 N.

 

 

For the given data:

 

By  (1)      aCx   =   [  ˗ Px  + μ N + Dx ] / m  =   1.1875 m/sec2 

 

By (3)          α  =   2 [  μ N  + Dy ] / m r    =  3.09375  rad/sec2    

 

 

Next calculate  aP  .     aP  =  aC  +  aP/C |n  +  aP/C |t  

 

Note:  aP/C |n   =  0  since disk starts from rest  i.e.  ω = 0

 

        aP  =  1.1875 i    +  α k  x ˗ r j  =    1.1875 i    +  3.09375   k  x ˗ 4 j  = 13.5625 i   m/sec2

 

Result:  Since aP  and  F  are in the same directions, slipping does not occur in the ˗ x-direction.

 

 

                               



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