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1. Question about the inertia matrix of a bar

I I was wondering whether anyone could help me out with this?
2. Question about the Triple Product

Homework Statement [/B] Homework Equations a⋅(b x a) = 0 The Attempt at a Solution Is my working below correct? In particular, can you apply the rCB to both the first part of the bracket (0.2j) and the second part (w x rCB) individually like that? My second question relates to: Is...
3. Question about the inertia matrix of a bar

Ah that makes sense! This question is from an exam paper set by my university's engineering department a few years ago, is there any way to determine that this rod is infinitely thin from the wording of the question? Does the ''uniform slender'' part suggest this? Also, I was wondering why...
4. Question about the inertia matrix of a bar

If the moment of inertia relative to the parallel axis is zero, then why is the moment of inertia about axis ZZ (in my data book) not 0? This axis is parallel to the cylinder?
5. Question about the inertia matrix of a bar

I understand that but the x'-x' axis in the question is parallel to the bar and not perpendicular? Thanks
6. Question about the inertia matrix of a bar

Homework Statement Homework Equations ml2/12 The Attempt at a Solution So according to my databook: The axis x'-x' in the question corresponds to axis ZZ in the databook image above. That means in terms of radius, the moment of inertia about axis x'-x' is mr2/2. So in light of this...
7. Vector Multiplication

Homework Statement Homework Equations RAO = b(Sinβj+Cosβk) The Attempt at a Solution [/B] The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple...
8. Determining the rank of a matrix

Homework Statement Homework Equations N/A The Attempt at a Solution I know that they got a rank of 2 since there are 2 linearly independent columns but what if we decided to count rows? In that case we would have 4 linearly independent rows which would suggest the rank is 4? How do we...
9. Inverse Laplace transform of 1/s

Homework Statement Homework Equations N/A The Attempt at a Solution The left hand side (red box) is the data sheet provided to us in the exam. The right hand side (blue box) is Wolfram Alpha. The data sheet says that the inverse Laplace transform of 1/s is equal to u(t) (i.e. the unit step)...
10. Transfer function of a second order system

Homework Statement Homework Equations The Attempt at a Solution I have done question 1.18 and I understand it completely. However, for question 2.5, I do not understand how they got G(s)? Why isn't the G(s) in question 2.5 the same as G(s) at the bottom of question 1.18? I asked my lecturer...
11. Response of a 2nd order system

That makes sense. Thanks
12. Response of a 2nd order system

Generally we've Y(s) = G(s)U(s) but in this case it's Y(s)=G(s)U(s) + another term. Is there a reason why we don't have the usual Y(s) = G(s)U(s) ?
13. Response of a 2nd order system

I understand that but how did this then lead to the conclusion which of the terms is which? Thanks
14. Response of a 2nd order system

Homework Statement Homework Equations N/A The Attempt at a Solution I understand how they got the answer and the calculations they did but I have 3 questions about this screenshot. 1) Why the box in red is the transfer function? Is there a way to tell this from the Y(s) = ... expression? 2)...
15. Inertia matrix of a homogeneous cylinder

Sorry for the late reply. I am still confused. I just want to know how they (mathematically) got from the left hand side to the right. I don't understand how integrating the left hand side yields the right hand side.
16. Inertia matrix of a homogeneous cylinder

I understand that but I mean how would one integrate those terms with respect to m? They aren't constants?
17. Inertia matrix of a homogeneous cylinder

What are y'^2 and z'^2? I don't know what to sub in for these (not sure what they represent?) so can't do the integral until I know them.
18. Inertia matrix of a homogeneous cylinder

Homework Statement [/B] Homework Equations N/A The Attempt at a Solution What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...
19. Dynamic Analysis of a 5 DoF robot

Homework Statement Homework Equations N/A The Attempt at a Solution I am confused as to where the ω3sin(θ)k term disappeared to? It is not included in the very last line? I asked my lecturer and he said it's ''constant'' but he kind of shrugged off the question. I understand everything...
20. Application of circularity of hybrid product

So -k·((-1)rCD x rBA)=(-1)(-k)·(rCD x rBA) = k·(rCD x rBA)? I was thinking it would be something along these lines but I wasn't sure how to pull out the negative when dealing with vectors.
21. Application of circularity of hybrid product

Ah I never noticed that! So -rCD·(k x rBA) = -k·(rBA x rCD) but I'm still confused in terms of how they got from -k·(rBA x rCD) to k·(rCD x rBA)? I know that A x B = -B x A so -k·(rBA x rCD) can be written as -k·(-rCD x rBA) and I'm guessing the two negatives cancel somehow but don't know how..
22. Kinematics of a four bar linkage system

Homework Statement Homework Equations N/A The Attempt at a Solution I have 2 (basic) questions about this system: 1) The question says that ωAB = ωABk, I understand that bold indicates vectors whilst the plain text indicates a magnitude so ωAB (magnitude) multiplied by k (direction vector)...
23. Application of circularity of hybrid product

Homework Statement http://photouploads.com/images/8ba21e.png {moderator's not: Inserted image so it's visible without having to follow a link} 2. Homework Equations a·(b x c) = b·(c x a) The Attempt at a Solution How did they get from the (b) to (c)? In particular, I am referring to the...
24. Calculating the maximum shear stress in a shaft

Homework Statement Homework Equations Torque = Force x Distance Shear stress = Force/Area 3. The Attempt at a Solution I know how to do this question as I've seen the mark scheme. However, initially I did it wrong. What I did was as follows: Torque = Force x Distance therefore...
25. Question about where a thermodynamics formula comes from

Homework Statement How do we obtain: w = q - Δh Homework Equations The Attempt at a Solution If you neglect the second half of the SFEE and simplify we get: What is the next step from the last line in the above image to w = q - Δh I mean dw/dt = dq/dt - Δh so if we multiply by dt we...
26. Gas turbine TS cycle question

Thanks for your reply. Unfortunately, I don't get that part either lol. Haven't encountered it in examples provided by my lecturer so far.
27. Gas turbine TS cycle question

Homework Statement Homework Equations N/A The Attempt at a Solution I am confused what 5-5b and 5b-6 represent in the above TS diagram. I know that 1-2 is compression, 2-3 is cooling, 3-4 is compression and 4-5 is regeneration (since these are indicated in the block diagram) but as for 5-5b...
28. Difference between the various COP formulae

I edited the above post to include the isostere question but I have now found out that it means constant concentration. However, I can't seem to edit the above post to reflect this hence I decided to post this message.
29. Difference between the various COP formulae

Homework Statement Homework Equations N/A The Attempt at a Solution My question is a simple one: how is the above equation for COPref different to the COPref equations I've already encountered (such as COPref = Qc/Win = (h1-h4)/(h2-h1). Is the above just a different form of these? Or is the...
30. Confused on a question about vapour refrigeration cycle

Homework Statement http://photouploads.com/images/ae1d2f.png Homework Equations N/A The Attempt at a Solution In the image linked above, I have copied and pasted 4 different slides. In the last slide, I am confused how they got the expression for T2 (the working out). I know that they did...