Soln Video 7/25

Prof, I think you may have made a mistake in this solution video. When you calculated the first w which was the angular velocity of "xyz" you said we would use this later, but when you calculated the alpha of the shaft you used the w of the shaft which contained wo (omega not). Which I think is wrong. This could possibly be why, when I put the numbers in to the final equations, I do not get the correct answers provided in the book. If anyone one else has had this problem and maybe figured out what im doing wrong. please let me know. Thanks

[Click here for a revised copy of the solution for 7/25. CMK]

Homework Problem 7/24

Suggestions:

• Attach XYZ to ground (fixed axes)
• Attach observer and xyz to boom.
  
• At the instant shown, xyz and XYZ are aligned.
  

Homework 7/27

I have been able to find all the values in this problem except for the a_B. The equation I am using is a_B = a_A + (a_B/A) + (alpha x r_B/A) + 2(omega) x (v_A/B) + omega x (omega x r_B/A). I have found that the only components not equal to zero would be a_A and omega x (omega x r_B/A) yet when I calculate I get an incorrect answer. Any ideas?

Homework Problems 7/10 and 7/21

Comments and suggestions:

• For each of these two problems, we need two sets of coordinates axes since one component of rotation is about a fixed axis and one component of rotation is about a moving axis. The problem statement for Problem 7/10 shows only one set. For the remaining discussion, I will refer to the observer and coordinate axes shown above for each problem: XYZ which is fixed, and xyz (and observer) attached to the panel in 7/10 and to the disk in 7/21. In each problem the XYZ and xyz axes are aligned with each other for the instant of interest.
• For each problem, write down the angular velocity, omega, of the observer. Differentiate omega to find alpha.
• In 7/10 use the following acceleration equation:  a_P = a_O + (a_P/O)_rel + alpha x r_P/O + 2*omega x (v_P/O)_rel + omega x (omega x r_P/O). With the observer attached to the panel, the observer does not see any motion for point P. Therefore, (v_P/O)_rel = (a_P/O)_rel = 0.
• In 7/21, replace "P" in the bullet item above with "B".

Problem 7/19 -- PLEASE READ

This problem asks us to find the "space cone" and "body cone". We are not covering these topics this semester. You are NOT required to find these for your homework problem submission.

Problem 7/15

Suggestions:
This problem is very similar to the problems that we looked at in lecture on Monday. The basic steps:

1. Attach observer/xyz to dumbbell.
2. The angular velocity (omega) of the observer has two components: Omega about the FIXED Z axis, and omega_P about the MOVING z axis: omega = Omega*K + omega_P*k
   
3. The angular acceleration (alpha) is simply the time derivative of the omega vector: alpha = Omega_dot*K + Omega*K_dot + omega_P_dot*k + omega_P*k_dot . The first three terms on the RHS of this equation are zero. For the fourth term use: k_dot = omega x k
4. For both parts you will need to convert the K over to i and k to get all components in terms of the same unit vectors. Let us know if you have any question on this conversion.
   

Problem 7/19

For solving this Problem 7/19, would it be better to use the method similar to the example on p.61 of the notes, or should we be using the velocity and acceleration equations that we have been using thus far? Thank you.

-Dale Szul-