Southperry.net
Angular Momentum - Printable Version

+- Southperry.net (https://www.southperry.net)
+-- Forum: Social (https://www.southperry.net/forumdisplay.php?fid=14)
+--- Forum: Rubik's Cube (https://www.southperry.net/forumdisplay.php?fid=58)
+--- Thread: Angular Momentum (/showthread.php?tid=39012)

Angular Momentum - 2147483647 - 2011-03-10

 Question 1


Angular Momentum - 2147483647 - 2011-03-13

Question 2:

[Image: 20110312224407.jpg]

I'm having trouble seeing why my answer is incorrect. According to my TA, the answer is:

L = (ωml^2)/12*[sin(φWink*cos(φWink i + sin(φWink^2 j]

In other words, my answer divided by a factor of 6. I'm having trouble understanding his solution:

 Spoiler

Help would be greatly appreciated.

Angular Momentum - 2147483647 - 2011-03-13

By the way, I don't understand tops and gyroscopes. I also don't understand torque in general. I know that the torque arises from τ = R x F, and that angular momentum is L = R x p, and a general diagram looks like this:

[Image: angular.png]

The above is great and all, and I'm comfortable when I see something like it. However, I'm having great difficulty understanding when I see something like this:

[Image: angular2.png]

Like what the hell? The torque can't come out of there, it's just not physically realizable. (If you don't understand what I'm talking about, open the next spoiler.

Because I'm actually desperate enough (and I'm literally freaking out about this angular crap for the final), I will reward a $10 NX card to the first person who can make me clearly understand the concepts of general rotations, tops, and gyroscope (all three) before TUESDAY (That is: Monday, March 14th, 2011 11:59 pm PST). Make diagrams, find online materials, whatever. If I understand your derivation, it's good. If multiple people try to help, I'll try to figure out how to distribute the rewards. (probably depending on the quality of the derivations).

Other: For tops, do not tell me that L is on the center of rotation, because that's not true. That's what my book tells me, and I'm not satisfied with that definition (nor do I understand this derivation). In fact, I'll post the page from my book.

 Spoiler

If your derivation looks like the above page, it doesn't count.

Angular Momentum - Russt - 2011-03-13

This all is kind of weird to me, but it seems like what they're referring to with the top is two kinds of rotation.

First, the top is spinning about its axis, which is L.

[Image: 4keC.png]

Second, if L is not completely vertical (if the top is tilted, like in the diagram), then the force of gravity will apply a torque to the top that will cause it to tip over.

[Image: 4keS.png]
(T = r cross g goes into the page; the top rotates about O, clockwise on the page. Imagine the top isn't spinning, it'll just fall down.)

How those two interact with each other to cause the axis of L to move around, I don't really understand, but hopefully my interpretation of the situation helps.

Also for question 1, it says angular momentum calculated about a point on its path, which would imply that the bottom point of your triangle is actually on the line of motion (so your triangle is degenerate, and phi = 90).

Angular Momentum - 2147483647 - 2011-03-14

Simple questions:

1. If I'm given τ and R, can I retrieve F﬩ by using F﬩ = τ x R ?
2. How can I use the above procedure (or some similar procedure) to retrieve R if I'm given T and F?

Angular Momentum - Russt - 2011-03-14

1. No. You can't retrieve F if you only know T and R.
2. Likewise, you can't retrieve R given T and F and no other information. You'd need either the direction or the magnitude of R (or something else). This is because T = R x F can be the same for different values of R. For example:

[Image: 4m1X.png]

R1 x F = R2 x F.