Chapter 2 Homework

Homework H2.B - Sp 25

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Problem statement
Solution video

DISCUSSION THREAD

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DISCUSSION and HINTS

The motion of point C is quite complicated. However, its path is defined by the combination of motion from the translation of A with the rotation of the plate. As expected, the velocity of C is always tangent to its path.


The solution for this problem is a straight-forward application of our rigid body kinematics equations relating the motion of point C back to point A:

vC = vA + ω x rC/A

where point A is translating to the right (positive x-direction) and the plate is rotating CCW at a rate of ω.

11 thoughts on “Homework H2.B - Sp 25”

  1. How should we define r_C/A, as during the rotation its location is constantly changing from point A.

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    1. In the problem statement, it says to use the location for the instant shown, so it is as simple as finding the vertical distance between A and C, which would be in the -j direction as I defined it.

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      1. I did this too, I had a -j component only for rC/A and a positive k component for angular velocity. which when crossed, left me with an answer solely in the i direction

    2. I agree with Joshua, I spoke with a TA and for the problems we are usually looking at the instance shown in the image so here you can ignore the movement shown in the hints and you can use Pythagoras to find the position vector of r_C/A in reference to what is shown in the problem statement

    3. Rc/a is instantaneous, so it is just the magnitude of the vertical distance between A and C - which is the sqrt(0.5^2+0.5^2). To get the vector Rc/a, you would multiply that magnitude with -j because the Rc/a vector points from the observation location A to point C.

  2. I'm feeling a little confused as to what direction the final answer should be in terms of positives and negatives.

    1. After I found rc/a it was as simple as crossing the w with the rc/a and adding the Va since they ended up being in the same direction. I found them to both be in the positive direction

        1. After you take the cross product between angular velocity (k) and the r c/a (-j), you will be left with an answer in the +i direction which you can then just add to Va since it is also in the i direction.

        2. The cross product between w(k direction) and R(-j direction) equals wR (i direction). So, the velocity will only be in the i direction.

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