Click here for a solution for Exam No. 1.
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Fall 2008 -- Purdue University -- West Lafayette, IN
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6 comments:
On the first multiple choice question, we can see that point B is purely translating.
From the path of point A, since the velocity is not tangent to the circumference of the disk we know that A has velocity from the rotation of the disk as well as from its translation.
We can conclude then that point B is the center of rotation of the disk which is also translating along the path of B.
Since A has this translational velocity, as well as a rotational one, can't we conclude that the velocity of A is greater than the velocity of B?
"From the path of point A, since the velocity is not tangent to the circumference of the disk we know that A has velocity from the rotation of the disk as well as from its translation"
The only situation that would have the velocity of A tangent to the circumference of the disk would be if the IC of the disk were at its geometric center (e.g., if the disk were pinned to ground at its center). Having an IC at any other place makes the velocity not tangent to the disk's circumference.
The point here is that one should not draw any conclusions on the direction of v_A based on the shape of the body. The shape of the body is generally not relevant in describing its motion.
"We can conclude then that point B is the center of rotation of the disk which is also translating along the path of B."
If B were the center of rotation (IC) of the disk, then the velocity of B would be zero (by definition). However, we know that the IC is at point C (based on the known information of the directions of motion for A and B). This is all we need then to determine the relative sizes of the speeds of A and B -- since B is further from C than A is from C, the speed of B must be larger than the speed of A.
The point here is that all one needs to know is the location of the IC of the rigid body in order to describe the relative speeds of various points on the body.
These are good questions. Let me know if you are not able to link up the IC vision of motion with your intuition.
I understand what you are saying and I agree with it, but I do have one final problem with the question.
The question states that the disk is a rigid body; however if you draw lines connecting the paths of A and B the distance between the two is clearly not constant (one's path is linear and the other's is parabolic).
Doesn't this violate the rigid body assumption and make this motion impossible?
I have added a figure of this problem to the original post. On this figure I have shown the line AB for the current position and three succeeding positions.
As you state, the distance AB must remain constant since A and B lie on the same rigid body. From this figure you can see that it is possible for the body to move over a range of positions with A on the circular path shown and with B on the rectilinear path shown.
Let me know if this does not answer your question.
Again, these are very good questions. It is important that you not only know how to work the problem but also that the results need to agree with your intuition. If they do not agree, keep asking questions! Thanks.
I was looking over the first problem in preparation for the final, and noticed that V_a is equal to 0. I wasn't quite sure why, I think it has something to do with the initial position, but am not quite sure, if you could help clarify this,I would appreciate it.
Thanks
It turns out that for this position, point A is the instant center of link OA. Therefore, vA = 0. The vector equation approach used in the solution supports this result.
Does this make sense?
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