## 11 thoughts on “4.1”

1. sousajp says:

How did you get the different values for the angular accelerations?

1. tutorpaul says:

I'm not sure I understand your question, could you elaborate?

1. ckeranen says:

I think what sousajp is trying to say is why did you have multiple angular acceleration and angular velocity values. You never explained why there are multiple values that can be solved for in part (a) and part (c) of the problem. Still a great video 😀

1. tutorpaul says:

Oh, that. It's been a while since I made this, so the details are a little fuzzy. This problem gives us more information than we actually need to solve it, and the numbers given aren't quite perfect. Notice that there we were able to derive two equations describing the angular velocity (and two equations describing the angular acceleration). Either of those should be equally valid, the fact that the numbers don't come out the same is a result of the inconsistency of the numbers given by the problem. The variation in the values we find by the two different equations is relatively small so we know that the numbers given in the problem statement are pretty good.

2. kkramer says:

How did you calculate the 4 values for theta double dot? Did you use both theta dot values found in part a? If so what was the reasoning behind that?

1. tutorpaul says:

I wrote some python code to solve these rigid body problems, so it wasn't too troublesome to execute. The reason I calculated with all permutations was so that the careful viewer following along at home would always be able to find the number they calculated. If the problem had been a little more precise then all of this controversy would have been avoided.

3. amorenojr says:

tutorpaul... the values you "MAGICALLY" choose, without explanation, to use for angular velocity and acceleration are the average of the two values you get when solving the cross product for omega in the z direction. If you do the actual calculation you get 248.038 and 247.914 not the values you wrote down. It is those values that average to get 247.976 rad/s and is used in the calculating the velocity of point P.

Furthermore, the average angular velocity that is the result, is used to solve for the two acceleration z direction results. Then those result, -363.219 and -390.908 rad/s^2, are averaged resulting in alpha = -393.563 rad/s^2 in the z direction. This value is then used to solve for the acceleration of point P which is 8167.19 m/s^2 in the x direction and -48.837 m/s^2 in the y direction.

These answers are consistent with the answers in the book, however much that is worth considering it is also riddled with error.

1. tutorpaul says:

Oh my, so salty. For starters, it is pretty magical that I put in 6 months of concerted effort to record, edit, and release all this content for free! You're welcome.

Second, there was nothing magical about the values I chose. They were chosen in a perfectly systematic manner. In fact I've just released the code that I used to calculate those numbers with such precise and repeatable specificity. I'm not certain what rounding regimen you are using to do your calculations, but my calculations are done without rounding on intermediate steps (using NumPy's floating point algorithms).

To the broader point, the numbers you cited are within approximately 0.03% of the numbers I cited. So we could probably say they are all well within the "just fine" range and set this quibbling aside.

In short, fight me bro!

1. amorenojr says:

Forgive me. I am incredibly frustrated with the delivery of this course considering the amount of money and time I have vested. The cliff hanging reason as to why you choose the values you did was enough to send me off. However, if you are interested, I can email you my work and we can discuss the content... The way I worked to problem gave me 0% error with that of the answer in the book (again, for what its worth). If you have an explanation as to why you choose the values you did I would like to know in order to add that tool to my belt. Shall we dance?

1. amorenojr says:

correction... ~0.3% error as well.

2. tutorpaul says:

I completely understand your frustration! I remember well your frustration from when I took the course, and I have seen that frustration on the faces of countless students when I was tutoring in ENPH (is everybody calling it Cain now?). That frustration is why this site exists at all.

Consider this your forum! Discussing your method here can only make it easier for future students taking this course! Please share what you've learned! I have a $\LaTeX$ plugin for WordPress here that will let you format your maths beatifully. I encourage you to use it! (wrap your maths in backslashed parentheses e.g. \ (\ddot\alpha = 5\dot\beta\ ) looks like $\ddot\alpha = 5\dot\beta$)

I feel like I've held up my end of that bargain in explaining my methods by posting the code, but I haven't yet explained what it does. In short, it iterates through all possible ways of calculating the unknown quantities given the imprecise and (if memory serves) over-constrained inputs. The output of the script shows the wide range of solutions that all conform to the problem statement:
Possible Angular Velocities: [247.957, 247.980, 247.980, 247.957] Possible Angular Accelerations: [-373.231, -394.591, -395.151, -401.344]
To me each of answers is equally correct. However, it is entirely possible that there is some bug in my code that could explain the $-373.231$ which feels like it is out of place.

I don't think this problem has a single True solution because it gives too much information, and because that information is not internally consistent. The author of the problem introduced their own rounding error into the fabric of the problem, and codified it as the official answer. I'll forgive you for not having learned that official answers always oversimplify problems (if you'll forgive me for being a patronizing ass).