Q2. The circular disk rolls to the left without slipping. The acceleration of A relative to B is aA/B = – 3 jm/s². Represent all answers below as vectors in Cartesian in terms of i and j. a) What is the instantaneous center of rotation of the disk? b) Determine the linear velocity of the center O of the disk. (Cartesian vector in terms of i and j) c) Determine the acceleration of the center O of the disk. (Cartesian vector in terms of i and j) d) Determine the linear velocity of point B. e) Determine the acceleration of the bottommost point on the disk, momentarily in contact with the ground. Hint: Assume that you do not know the angular velocity wk and the angular acceleration ak. Then, write the equation for the relative acceleration aR = a, - ap in terms of the scalars w and a. Expand everything. You will now have a single vector equation with i and j components. This will give two scalar equations, one for i component, one for j component. You can now solve for w and a. Once you've done so, you can solve for everything else. A 150 mm L 150 B 200 mm mm

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Q2. The circular disk rolls to the left without slipping. The acceleration of A relative to B is
aA/B = – 3jm/s². Represent all answers below as vectors in Cartesian in terms of i and j.
a) What is the instantaneous center of rotation of the disk?
b) Determine the linear velocity of the center O of the disk. (Cartesian vector in terms of i and j)
c) Determine the acceleration of the center O of the disk. (Cartesian vector in terms of i and j)
d) Determine the linear velocity of point B.
e) Determine the acceleration of the bottommost point on the disk, momentarily in contact with
the ground.
Hint: Assume that you do not know the angular velocity ok and the angular acceleration ak.
Then, write the equation for the relative acceleration aR = a, - ap in terms of the scalars w
and a. Expand everything. You will now have a single vector equation with i and j
components. This will give two scalar equations, one for i component, one for j component.
You can now solve for w and a. Once you've done so, you can solve for everything else.
150 mm
150 B
200 mm
mm
Transcribed Image Text:Q2. The circular disk rolls to the left without slipping. The acceleration of A relative to B is aA/B = – 3jm/s². Represent all answers below as vectors in Cartesian in terms of i and j. a) What is the instantaneous center of rotation of the disk? b) Determine the linear velocity of the center O of the disk. (Cartesian vector in terms of i and j) c) Determine the acceleration of the center O of the disk. (Cartesian vector in terms of i and j) d) Determine the linear velocity of point B. e) Determine the acceleration of the bottommost point on the disk, momentarily in contact with the ground. Hint: Assume that you do not know the angular velocity ok and the angular acceleration ak. Then, write the equation for the relative acceleration aR = a, - ap in terms of the scalars w and a. Expand everything. You will now have a single vector equation with i and j components. This will give two scalar equations, one for i component, one for j component. You can now solve for w and a. Once you've done so, you can solve for everything else. 150 mm 150 B 200 mm mm
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