Homework H2.A.38

DISCUSSION

Note that with the disk not slipping on the outer cable, and with section BC of that cable being at rest, the velocity of point C on the disk has zero velocity. This means that the disk rolls without slipping on the cable, which is the same is it were rolling without slipping on a fixed vertical wall.

With the above in mind, consider the following:

  • Let M represent the point on the left side of the pulley from which the outer cable leaves contact with the disk. Note that M is moving vertically upward with a speed of vA.
  • Write a rigid body kinematics equation relating the motion of points C and M: vM = vC + ω x rM/C . That equation will produce an expression for ω, the angular speed of the disk.
  • Then, you can use vN = vC + ω x rN/C and  vH = vC + ω x rH/C to find the velocities of point N and H on the disk. Since the inner cable does not slip on the disk, then vN = vD and vH = vQ.
  • Also,  vE = vC + ω x rE/C.

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