| Problem statement Solution video |
DISCUSSION THREAD
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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
Good morning! Both of the links attached to this problem send you to the same YouTube video, and we cannot view the video because it is currently private. (I assume the link is sending us to the solution video, which is why it's private)
The link is now fixed. Let us know if you continue to have problems accessing the problem statement. Thanks for letting us know of the problem.
Does "θ = 0 = constant" mean there is no angular velocity or acceleration or does it mean that at this instant, theta = 0?
I believe it means that at this instant theta = 0. Since it is constant, theta dot and theta double dot are also zero, but there can still be angular velocity and acceleration due to omega 0 and 1.
jbrooken: Your interpretation of this is correct.
So just to clarify the change, the motor is now fixed facing right and the xyz and XYZ axes are now aligned? Or am I misinterpreting something?
Yes, this interpretation is correct. Because the motor is now fixed to the horizontal axes (theta=0=constant), the xyz coordinate system and the XYZ coordinate system are now alligned for all time.
For the past two homework assignments, H3.E and F the solution videos are private, it will not let me access them.
The "late" submission time for H3.E/F is noon today. These videos will be released and viewable after that time.
Since ω0 is rotating about the fixed J axis, should our final answer for angular acceleration be related to the fixed J axis, or should we use a vector projection to relate it to the disk axis? Thanks.
Nevermind, I see that with with theta being changed to 0, it will work out to where J = j .
For finding the velocity at A, if the observer is on the disk wouldn't the velocity relative to the observer be zero since it looks stationary to the observer?
Yes I believe your interpretation is correct.
is Va only in the little j?
You need to use the full form of the MRF velocity equation (provided above in the Discussion and Hints) to find v_A.
I suspect that the answer is NOT only in the lower case j direction.
How would you figure out v(A/O)rel?
To what body is the observer attached? If the observer is attached to the disk, the both the observed velocity and acceleration of A are zero.
For part B are we using the ω calculated in part A?
You use the angular velocity of the observer. Who is your observer and to which rigid body is the observer attached? That is the omega that is used here.
I assume the point O mentioned in the hints is on the lowercase x-axis on the disk. How can we find its velocity? Its movement seems to be almost as complicated as A's.
The point O mentioned in the Discussion is at the intersection of the vertical shaft about which the motor housing rotates and the motor shaft to which the disk is attached.