Homework H3.B.12 | ME 274: Basic Mechanics II - Purdue University

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CHANGE IN PROBLEM STATEMENT:  Please use θ = 0 = constant when solving this problem.

DISCUSSION and HINTS

For your work on this problem, it is recommended that you use an observer attached to the disk. The observer/disk has two components of rotation:

  • One component of ω0 about the fixed J-axis.
  • The second component of ω1 about the moving i-axis.

Write out the angular velocity vector ω in terms of the two components described above.

Take a time derivative of ω to get the angular acceleration α of the observer/disk. When taking this derivative, you will need to find the time derivative of the unit vector i. How do you do this? Read back over Section 3.2 of the lecture book. There you will see: i_dot = ω x i, where ω is the total angular velocity vector of the disk that you found above.

Velocty of point A The motion of A is quite complicated. To better understand the motion of A, consider first the view of point A by our observer who is attached to the disk – what does this observer see in terms of relative velocity: (vA/O)rel?

With this known relative motion, we can use the moving reference frame velocity equation:

vA = vO + (vA/O)rel + ω x rA/O

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