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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 K-axis.
- The second component of ωdisk about the moving j-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 j. How do you do this? Read back over Section 3.2 of the lecture book. There you will see: j_dot = ω x j, where ω is the total angular velocity vector of the disk that you found above.
Acceleration 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 and relative acceleration: (vA/B)rel and (aA/B)rel?
With this known relative motion, we can use the moving reference frame acceleration equation:
aA = aB + (aA/B)rel +α x rA/B + 2 ω x (vA/B)rel + ω x (ω x rA/B)
In finding the acceleration of B, aB, note that B moves with a constant speed on a circular path centered on point O. Use the path description to find aB. WARNING: Although B moves with a constant speed, its acceleration is NOT zero.