Is the transfer from 2D mechanics to 3D mechanics intimidating?

  • Context: Undergrad 
  • Thread starter Thread starter Femme_physics
  • Start date Start date
  • Tags Tags
    2d 3d Mechanics
Click For Summary

Discussion Overview

The discussion revolves around the transition from 2D to 3D mechanics, exploring the challenges and learning curve associated with this shift. Participants share their thoughts on whether the skills developed in 2D are applicable in 3D contexts, and they discuss specific problems related to calculating forces and moments in three dimensions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Some participants express curiosity about the additional learning required when moving from 2D to 3D mechanics.
  • Others argue that 3D mechanics can be managed with conventional algebra, but vector algebra is more convenient, especially when familiar with parametric notation.
  • One participant suggests that classical mechanics is inherently 3D, and the transition is not as difficult as it seems, as many problems can be simplified by identifying symmetries.
  • There are discussions about specific problems involving moments and forces, with participants debating whether to use diagonal or horizontal distances in calculations.
  • Some participants mention the inertia tensor as a potentially intimidating aspect of 3D mechanics, but they also note that it is easier than it sounds.
  • There is a suggestion that while many simple systems can be reduced to 2D, there are exceptions, such as modeling charged particles in magnetic fields.
  • Participants share their experiences with specific problems and seek clarification on how to visualize and calculate forces in 3D scenarios.
  • There is a mention of a potential error in a solution manual, leading to further discussion about the correctness of certain diagrams and calculations.

Areas of Agreement / Disagreement

Participants generally express a mix of reassurance and uncertainty regarding the transition from 2D to 3D mechanics. While some agree that simplifications are often possible, others highlight that not all problems can be reduced to 2D, indicating a lack of consensus on this point.

Contextual Notes

Some discussions involve specific calculations and visualizations that may depend on individual interpretations of diagrams and problem setups. There are references to solution manuals that may contain errors, which adds to the complexity of the discussion.

Who May Find This Useful

This discussion may be useful for students transitioning from 2D to 3D mechanics, educators seeking to understand common student concerns, and anyone interested in the nuances of applying mechanics in three dimensions.

Femme_physics
Gold Member
Messages
2,548
Reaction score
1
How much more than is to learn when you go from 2D to 3D? I'm curious to know whether all these problems I solve in 2D are less helpful for when we move to 3D, where there are more elements?
 
Physics news on Phys.org
3D can be managed using conventional algebra alone, but it is more convenient to use vector algebra using dot and cross products. So if you have done 2D using vectors, then 3D is a reasonably simple extension of that. You also need to be familiar with parametric notation.
 
Femme_physics said:
How much more than is to learn when you go from 2D to 3D? I'm curious to know whether all these problems I solve in 2D are less helpful for when we move to 3D, where there are more elements?

There should be absolutely no difficulty.Actually there isn't really a transition from 2D to 3D all classical mechanics is in 3D you sometimes ignore one or 2 dimensions.
 
Yes, many problems you will encounter will allow you to reduce the number of dimensions by some symmetry of the problem. You just have to identify the symmetry.

Otherwise it just like 2D, just with potentially more variables.
 
Thanks for the reassurance. So I can always "reduce" the problem to 2D, is what you're saying?


That reminds me, I've been staring at a certain problem since my first semester trying to think which distances to take when I calculate the arm of the force in the middle, the 600 [N], to point A. Do I take the diagonal distance here from 600 to A, or do I just use the horizontal one to the wall (that being 0.45)?

http://img860.imageshack.us/img860/6118/40893341.jpg
 
Last edited by a moderator:
You can do either but you must be consistent when forming the equation.

That means that all other moments in the equation must be calculated about the same point or axis.

In this problem it is probably best to take moments about the line through AB and use the perpendicular distance to that line ie the perp dist to the wall.
 
Ah, so in this case it's 0.45 + 0.6? Or just 0.45?
 
The force on the plate has a moment of

600 x 0.45 about the z axis (line through AB)

600 x 0.6 about the x-axis (line through BD)

It has zero moment about the y-axis since it is parallel to it.


and so on
 
The one slightly intimidating thing about 3D is the inertia tensor but it is actually far easier than it sounds (and its dynamics).

For your problem, yep, what studiot says, you can pick any line as axis of rotation, the sum of moments around that axis will be zero. I'd use diagonal BC as axis.
Also, don't forget that force on A is pulling that hinge out of the wall. That may be what you need to calculate?
 
  • #10
Femme_physics said:
Thanks for the reassurance. So I can always "reduce" the problem to 2D, is what you're saying?

No, this is not always possible, but most simple systems will allow this. The simplest example I can think of where you cannot reduce the number of dimensions is when modelling the motion of a charged particle in a magnetic field, in which the force is always acting perpendicular to the direction of motion, and even then you can sometimes (for example if the field is homogenous) make a coordinate transformation which allows you to reduce the problem to 2 dimensions.
 
  • #11
Dmytry said:
The one slightly intimidating thing about 3D is the inertia tensor but it is actually far easier than it sounds (and its dynamics).

For your problem, yep, what studiot says, you can pick any line as axis of rotation, the sum of moments around that axis will be zero. I'd use diagonal BC as axis.
Also, don't forget that force on A is pulling that hinge out of the wall. That may be what you need to calculate?

That's okay, I was just giving an example I wasn't trying to solve the problem. Your replies cleared it :)

Thanks.
 
  • #12
Femme_physics said:
That reminds me, I've been staring at a certain problem since my first semester trying to think which distances to take when I calculate the arm of the force in the middle, the 600 [N], to point A. Do I take the diagonal distance here from 600 to A, or do I just use the horizontal one to the wall (that being 0.45)?

For a 3D situation like this, you are not taking moments about a point, you are taking moments about a line. In a 2D problem, the line is always perpendicular to the 2D plane, so the there isn't an obvious difference between the line and the point where it intersects the plane.

If you take monents about the line AB to get an equation for the forces at C, you use the perpendicular distance from AB. If yuu take moments about AC (which would be a good way to find the vertical reaction at B) you use the perpendicular distance from AC.
 
  • #13
AlephZero said:
For a 3D situation like this, you are not taking moments about a point, you are taking moments about a line. In a 2D problem, the line is always perpendicular to the 2D plane, so the there isn't an obvious difference between the line and the point where it intersects the plane.

If you take monents about the line AB to get an equation for the forces at C, you use the perpendicular distance from AB. If yuu take moments about AC (which would be a good way to find the vertical reaction at B) you use the perpendicular distance from AC.

We recently started 3D so I finally understand this comment.

May I ask though, taking the yx view for the diagram I posted above, is CE drawn like that?

http://img862.imageshack.us/img862/7495/ce1.jpg
Or like this?

http://img535.imageshack.us/img535/2858/ce2v.jpg IMO it's the latter that's correct
 
Last edited by a moderator:
  • #14
Femme_physics said:
taking the yx view for the diagram I posted above, is CE drawn like that?

Perhaps you should include the stick and the wall in your drawing, and then treat it as a regular 2D problem.
If you would do that, would you get a visual cue from it? :wink:
 
  • #15
Good point. Then it should be the first one, I reckon, yep. I agree, first one :)
 
  • #16
Femme_physics said:
Good point. Then it should be the first one, I reckon, yep. I agree, first one :)

I reckon I agree! :smile:
 
  • #17
Last edited by a moderator:
  • #18
This looks intimidating!
So you were already looking at the solution manual? :wink:

Did you try to solve the problem yourself?
What did you find?
Did you run into any problems?
 
  • #19
Well, I guess just lingering curiosity since I got a bit confused as to how to solve it, but I was being kinda stupid because if I'd thought a bit more I'd find out it's really equation. Just take the yx view and do sum of all moments on O.

But I decided to look at the manual and that's when the question came up... because if I do sum of all forces on X it DOES exist, whereas in their diagram it doesn't. What's the deal?
 
  • #20
Perhaps you have found an error in the solution manual.

Doesn't that thought excite you? :smile:

Show them wrong gurl!

(Quickly before someone else here proves me wrong! :wink:)
 
  • #21
I guess if someone didn't fix you after so long I must be correct :smile:

Getting back to the original diagram

http://img860.imageshack.us/img860/6118/40893341.jpg [/QUOTE]

In the YZ view. I think the left drawing is the correct one. Correct?

attachment.php?attachmentid=36775&stc=1&d=1309245965.jpg
 

Attachments

  • yofi.jpg
    yofi.jpg
    20 KB · Views: 573
Last edited by a moderator:
  • #22
Good morning Fp! :smile:

Femme_physics said:
Getting back to the original diagram

In the YZ view. I think the left drawing is the correct one. Correct?

Left! :wink:

Femme_physics said:
I guess if someone didn't fix you after so long I must be correct :smile:

There is a little more to it, but some things are best experienced rather than be told.
(The others in this thread seem to agree, because I'm sure they know what's going on.)

However, since I love you so much and you are apparently very reluctant to do the work, I'll give you a hint. ;)

Suppose you snip the cord CD, what would happen with the construction? Would it still be in equilibrium or not?
 
  • #23
I like Serena said:
Good morning Fp! :smile:



Left! :wink:



There is a little more to it, but some things are best experienced rather than be told.
(The others in this thread seem to agree, because I'm sure they know what's going on.)

However, since I love you so much and you are apparently very reluctant to do the work, I'll give you a hint. ;)

Suppose you snip the cord CD, what would happen with the construction? Would it still be in equilibrium or not?


Of course not, it would be pulled over by TAB

And I'm not "very reluctant to do the work"! And I learn tons of things the hard way, and I like it. Sometimes I try it the easy way because sometimes the easy way works too and enlightens me too. :smile:

And I'm actually trying to solve it right now, after solving 7 questions on my own yesterday (statics+dynamics including 3D) from a test that was last year. So am always practicing to keep myself in shipshape :biggrin:

Much of course thanks to you!

Anyway, off with the verbosity and on to physics :smile:

Yes, to repeat, it would be pulled over by TAB :wink:
 
  • #24
Femme_physics said:
Yes, to repeat, it would be pulled over by TAB :wink:

If TAB pulls it over, what would happen to the cord AD?
 
  • #25
It pulls Tab preventing its pull
 
  • #26
Femme_physics said:
It pulls Tab preventing its pull

Is the system then still in equilibrium?

And what if we snip AD instead of CD?
 
  • #27
[/quote]Is the system then still in equilibrium?
Is the system then still in equilibrium?[/quote]

Definitely not,
And what if we snip AD instead of CD?
There would be nothing to prevent its torque. And after it begins its torque then CD will pull it to its way.
 
  • #28
Femme_physics said:
It pulls Tab preventing its pull

Femme_physics said:
Is the system then still in equilibrium?

Definitely not,

:confused:
First you said Tad prevented the pull of Tab, and then you said it is not in equilibrium?
 
Last edited:
  • #29
yes, if we snip it then it won't be in equilibrium anymore

TCD does indeed prevent the pull.

I don't see how my affirmations are conflicting?
 
  • #30
Femme_physics said:
yes, if we snip it then it won't be in equilibrium anymore

TCD does indeed prevent the pull.

I don't see how my affirmations are conflicting?

So we snip CD.

If the system is not in equilibrium anymore, that would mean that point A starts moving.
In which direction will it move then?

If this movement is prevented by Tad, then that would mean the system is still in equilibrium.
Edit: the movement is prevented by a combination of Tad and Foa.
 
Last edited:

Similar threads

Undergrad [Questions] Modeling a Baseball Pitch Trajectory in 3D Space
  • · Replies 1 ·
Replies
1
Views
2K
3D printers for mechanical engineering
  • · Replies 1 ·
Replies
1
Views
2K
2D vs 3D Method of Characteristics for Rocket Nozzle Design
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Why does quantum mechanics believe that gravity is a field?
  • · Replies 10 ·
Replies
10
Views
3K
Classical Undergrad book on Classical Mechanics
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Statistical physics in 2D world: How to simulate gas and its interaction with objects? (game design)
  • · Replies 6 ·
Replies
6
Views
2K
How Does Dimensionality Affect Phonon Polarizations?
  • · Replies 1 ·
Replies
1
Views
1K
High School Answer: Basic Physics Question - Free Fall in 2D or 3D?
  • · Replies 22 ·
Replies
22
Views
4K
Undergrad Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
  • · Replies 5 ·
Replies
5
Views
4K
Heat transfer in wing by anti-ice system using hot air in piccolo tube
  • · Replies 6 ·
Replies
6
Views
2K