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DISCUSSION and HINTS
The disk has two components of rotation:
- One component of ω1 about the fixed J-axis.
- The second component of ω2 about the moving k-axis.
Part (a)
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 bar. When taking this derivative, you will need to find the time derivative of the unit vector k. How do you do this? Read back over Section 3.2 of the lecture book. There you will see: k_dot = ω x k, where ω is the total angular velocity vector of bar OA that you found above.
Part (b)
Here you will use the MRF kinematics equations of:
vP = vO +(vP/O)rel + ω x rP/O
aP = aO + (aP/O)rel + α x rP/O + 2ω x (vP/O)rel + ω x (ω x rP/O)
For these equations, employ an observer on the disk. The angular velocity and angular acceleration of the observer are the same as the ω and α of the disk found in Part (a). What are the relative velocity and relative acceleration terms ((vP/O)rel and (aP/O)rel ) in these equations? These represent the velocity and acceleration of P as seen by our observer. As our observer moves with the disk and with P being on the disk, what motion does the observer see for P?