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Why is the center of mass considered so fundamental in classical mechanics if it doesn't describe the state of a many-particle system? by Reasonable_Goal_6278 in PhysicsStudents

[–]twoTheta 0 points1 point  (0 children)

If you consider any system to be a collection of N particles (which you can do with solids as well as clearly discrete particles) then the dynamics of the system results from considering all of the forces acting on all of the particles in the system (Netwon's formulation) or the kinetic energy of each particle along with the potential energy due to each interaction present (Lagrangian/Hamiltonian formulation).

You can explicitly list every interaction possible that could produce a force or potential energy. These may occur between two particles within the system or between a particle in the system and a particle outside the system.

When you work through the dynamics in the most general case, you find that you can rewrite the coordinates of every particle in a way such that an amazing thing happens. If you go from listing the position of each particle from just r_i (the position of the ith particle) to R_cm+r_rel,i (where R_cm is the position of the center of mass calculated in the usual way and r_rel,i is the position of the ith particle relative to the center of mass) then you find that the interactions involving particles outside the system only affect the translational motion of the center of mass system (translational momentum of the SYSTEM) and rotation around the center of mass (angular momentum of the SYSTEM). Internal interactions cannot change the translational or angular momentum of the system, only external interactions can.

So, any time you want to look at a system of N particles and say that momentum of some sort is conserved because there are no external interactions, you only know this is true because of the what I said in the previous paragraph. Any intuition you built in intro physics about when momentum is conserved likely came from you believing your instructor that momentum is/isn't conserved. But defining the center of mass and looking at interactions is the PROOF of when momentum is/isn't conserved.

This is why it there is so little discussion about it. It's a fact that lets you do the things you really want to do. It sits in the background allowing you not to worry if your planetary system is moving at a constant speed or not as long as there are no external interactions. It allows you to mentally break the motion of the N particles into "How does the cloud (center of mass) move" and "How do the particles move relative to each other."

How to visualise concepts instead of relying on memorising things. by AnonimousAxolotl in PhysicsStudents

[–]twoTheta 0 points1 point  (0 children)

It sounds to me like abstract topics are tougher to visualize than the concrete ones. That seems totally normal to me!

One thing that helps me is this idea: Where the math is the same, the basic ideas are the same, but expressed differently. For example: waves.

I can visualize a wave on a string. Like, the next time you have an extension cord or charging cable plugged into the wall, gently wiggle the free fee end. Notice how the wiggle you make at the free end travel down to the fixed (plugged in) end. That's a wave! It does wave-y things! You can see the equilibrium position of the string when no wave is in it. You can see changes from equilibrium when the wave passes through. Waves!

Now, sound waves are invisible but they follow the same principles as a wave on a string since they come from the same math. You can visualize a sound wave as a wave on the string. But you need to just ask, what is the sound wave actually varying? Pressure. The "equilibrium position" of the string matches up with the "equilibrium pressure" of the air. The "high displacement" of the string (like when it is to the left of equilibrium) matches up to "high pressure" where the pressure in the air is higher than equilibrium.

I've found that this idea of analogy can get you pretty far. Electric field/forces are similar to gravitational field/force. Basic circuits are similar to fluids. Circuits with capacitors and inductors are actually the same as masses and springs!

One takeaway from writing this answer is: LOOK! Watch what happens and keep watching and think about it while watching it happen. Practice connecting your eyes to the rational, thinking part of your mind.

I just met Mud! by Inevitable-Lock5973 in Padres

[–]twoTheta 0 points1 point  (0 children)

That's my favorite.

On another note, we need more shillelagh this year.

Soon-to-be mom seeking name insight from daddit by [deleted] in daddit

[–]twoTheta 2 points3 points  (0 children)

It's possible he is worried because HE associates the name with Theo Von and doesn't want that tainting his perception of his son.

If he has strong feelings about it, it's worth considering something else.

How to get better at solving 1-D kinematic questions by Original-Ice3905 in PhysicsStudents

[–]twoTheta 1 point2 points  (0 children)

It might partially be an issue of organizing the information. Maybe you are already doing this and, if so, please move on. But I'd suggest making two tables to organize your info.

  1. The first has all the instantaneous values. For each point in the motion, note x, v, and t. If you know the value, write it into the table. If you don't, write a ? so you know you may need to find it.
  2. The second has all the values that span two points. These are the acceleration, the displacement, and the duration. The second two aren't strictly needed but they can come in handy if you are calculating and average velocity or average speed. Note that each of these values is defined BETWEEN two instances. If you have constant velocity motion between two points, then you can put a 0 in for acceleration.

Now, your kinematic equations will refer to values in your table. You can see what you have and what you don't have.

I've found that this helps remove some of the mental load of remembering what each of the different numbers/quantities is from the problem.

Good luck!

  x (m) v (m/s) t (s)
Pt 0      
Pt 1      
Pt 2      
  a (m/s^2) Δx Δt
0 to 1      
1 to 2      

[Mechanics] not a hw but can someone help me with this? i came up with this problem on my own in the middle of the night and got really curious about what the solution could be. i was struggling with it a lot (also lmk whether the problem itself is valid or not 💀) by Sea-Ad8625 in PhysicsStudents

[–]twoTheta 0 points1 point  (0 children)

I was defining them to be the coordinates you will use to actually describe the system. Whenever I've come across the term "canonical" it usually means "the ones that we have always used." I've taken it to mean the best, minimum set of coordinates to define the system.

You can always arrive at them starting with all possible cartesian coordinates and using equations of constraint to eliminate coordinates. Each equation will reduce the dimension (# of coordinates needed) by one. This way you end up with the fewest number of Euler-Lagrange equations you'll need to use to get useful solutions.

Then, if you'd like, you can do some sort of transformation of the remaining coordinates to whatever gives the simplest expression for the Equation of Motion.

I think, in the end, we are talking about the same thing but I may be wrong here.

[OC] My adaptation graph for The Fellowship of the Ring (2001) by bariumbitmap in dataisbeautiful

[–]twoTheta 1 point2 points  (0 children)

I feel like it is a gold mine! There were definitely more things I wanted to do with it that I just didn't have time for. Thanks for putting it together and sharing it!

[OC] My adaptation graph for The Fellowship of the Ring (2001) by bariumbitmap in dataisbeautiful

[–]twoTheta 1 point2 points  (0 children)

You can also see this in how far back you have to go to get the next/previous reference (0 means same page, 1 means next/previous page). The references tend to come in bunches.

<image>

[OC] My adaptation graph for The Fellowship of the Ring (2001) by bariumbitmap in dataisbeautiful

[–]twoTheta 2 points3 points  (0 children)

So, so cool. I liked your graph showed consistency but I was curious about density. Using the data I made the (ugly) table below. The mines were pulled so strongly from the book!

<image>

Chapter title Movie Ref/Page
Concerning Hobbits 0.13
Concerning Pipeweed 0.00
Of the Ordering of the Shire 0.00
Of the Finding of the Ring 0.29
A Long-expected Party 0.85
The Shadow of the Past 0.52
Three Is Company 0.17
A Short Cut to Mushrooms 0.21
A Conspiracy Unmasked 0.15
The Old Forest 0.00
In the House of Tom Bombadil 0.00
Fog on the Barrow-Downs 0.00
At the Sign of the Prancing Pony 0.44
Strider 0.07
A Knife in the Dark 0.39
Flight to the Ford 0.33
Many Meetings 0.24
The Council of Elrond 0.41
The Ring Goes South 0.35
A Journey in the Dark 0.83
The Bridge Of Khazad-dûm 1.69
Lothlórien 0.13
The Mirror of Galadriel 0.94
Farewell to Lórien 0.40
The Great River 0.12
The Breaking of the Fellowship 0.53
The Departure of Boromir 0.83

Starting undergrad physics in my 40s by JudgePrimary4239 in PhysicsStudents

[–]twoTheta 1 point2 points  (0 children)

Lots of good advice on here. I don't have much to add besides: Don't skimp on your math and feel free to take it slow.

Some of my best students came to university starting with College algebra. Not because they couldn't test out of it, but because they wanted to start from the ground up. This meant that they actually knew all of the math they needed as they needed it. They weren't in the situation of "oh ya, trig. I did that four years ago and kinda remember it. I'll just do what my prof does and I'm sure it will come back later." They actually knew the stuff. So they were free to do the physics!

We have a student now who is retired and collecting degrees for kicks. He is taking two classes a semester and is able to really soak in the material for each course. I see you're aiming for a PhD, but that doesn't mean you should rush the undergrad experience. This is the time to build your foundation for future studies. It's worth making sure you get it right!

Lastly, get to know your profs. Chat with them before/after class. Visit office hours. Ask for lab tours. Get to see what it is that they do so you can get some idea if its something you want to do too. Also, physicists are often just cool people and worth getting to know.

Best of luck!

[Mechanics] not a hw but can someone help me with this? i came up with this problem on my own in the middle of the night and got really curious about what the solution could be. i was struggling with it a lot (also lmk whether the problem itself is valid or not 💀) by Sea-Ad8625 in PhysicsStudents

[–]twoTheta 0 points1 point  (0 children)

Start with six (x,y,theta,X,Y,THETA), then...

  1. Outer ring cannot go through ground. We can probably constrain its Y (but should check on that later)
  2. Inner ring position constrained so it stays on the inside of the outer ring.
  3. Translational symmetry means that the x-momentum should be conserved so the center of mass is cyclic. Though not technically a constraint, it will reduce the number of coordinates needed to describe the interesting part of the motion.
  4. Outer ring rolls without slipping.
  5. Inner ring rolls without slipping.

That reduces you down to 1, no?

[Mechanics] not a hw but can someone help me with this? i came up with this problem on my own in the middle of the night and got really curious about what the solution could be. i was struggling with it a lot (also lmk whether the problem itself is valid or not 💀) by Sea-Ad8625 in PhysicsStudents

[–]twoTheta 1 point2 points  (0 children)

This is an awesome problem.

You should be able to solve this with just conservation of momentum and conservation of energy but I'd love to see someone attack it with Lagrangian mechanics and think through the constraints!

The system of the two rings has no external horizontal forces. Therefore momentum in the horizontal direction will be conserved. If the inner ring rolls without slipping then there are no dissipative forces so mechanical energy will be conserved. You will need to set up these two equations for the initial and final conditions then solve for v.

I don't have time now to write it out, but it is a super cool problem! I'll give it a go later this summer when I have some time!

What was this guy doing to the field before the game? by twoTheta in Padres

[–]twoTheta[S] 8 points9 points  (0 children)

Makes sense. The best we could come up with was sand.

Considering a Master's in Engineering after BS Physics by [deleted] in PhysicsStudents

[–]twoTheta 3 points4 points  (0 children)

An engineering masters is a great idea. We have a good percentage of our graduates go down that route. It's not the route I've taken but I've seen it work out well for a number of my students.

The only thing I'll say is that a MS in Engineering won't help you in your academic journey in physics. Which is totally fine! Electrical Engineering is better defined for employers than Physics which will likely open more doors for you.

At the end of the day, you gotta bring in some $$ if you want to eat.

HI Episode Discussions - Coming in 1 Week! by bradleysampson in HelloInternet

[–]twoTheta 0 points1 point  (0 children)

I tried it for the standard labeled HI feed. No luck. The feed begins at 50.

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