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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