Circular motion related to 1 dimension?

[melkor]

Alright, I have wondered this for a very long time and probably thought about it for longer than I should have but the more I think about it, the more I seem to be correct and the more frustrating it is to talk to people about it...

Anyways, I'm sure everyone has heard of the saying "lefty loosy, right tighty" and that it usually comes up in conversation when tightening/loosening something around the house. Anyways, for the life of me, I cannot comprehend how this can work at all. Basically you are converting a 2 dimensional rotation into 1 dimensional motion. Given the correct scenario I can understand how this may seem to work (at least for half of a rotation) but it completely blows up during the second half of the rotation. This is how I think of it.

Just using the screw/screwdriver scenario, if you imagine that you start with the screwdriver bound to a screw with a little black mark on the head of the screw driver in the 12 o'clock "initial" position. With your hand, you start to turn the screwdriver so the black mark rotates in the clock-wise position until it hits the 3 o'clock position (1/4 turn). This logically seems like it is going in the "right" direction as the dot on the screwdriver moved closer to the "right" side of the room. Moving the screwdriver another 1/4 turn to the 6 o'clock position however moves this black dot away from the right side and thus it moves closer to the left side (relative to the 3 o'clock position). If you do this 2 more times, obviously you start back where you were thus 1/2 of the time you were moving to the "right" and 1/2 of the time you were moving to the "left".

The scenario probably was not necessary as I imagine you all have a very solid understanding of turning a facet handle, or screwing in a screw, but I just wanted to make sure...Regardless, I have pretty much given up on trying to tell this to other people as they generally just blow this off without even thinking about it and say something to the effect "well, everyone says this so I doubt it's wrong...". So please, if anyone can educate me on either a.why I am wrong and why this actually does work, or b.give me a better way to explain it to people so they actually believe me, I would be very much appreciative.

On a side note, I'd rather not have to just use the scenario where 2 people on opposites sides of a glass floor are watching something turn and thus each person see's either counter-clockwise or clockwise thus giving a left/right turn appearance depending on location. I feel there is a better way of explaining it than that, I just haven't come up with it yet...

I know this is somewhat sad but it is so frustrating to me when I hear people say this as I quickly rebuke with my answer that a 2d rotation cannot/should not be turned into a 1 d motion. Also, I consider myself fairly well educated (in 2nd year of medical school) with a few semesters of physics back in undergrad so if this does involve some complicated concepts/equations to adequately prove it, I feel I should be able to at the very least learn it without too much trouble. Thank you very very much for your thoughts!

 

[berkeman]

Alright, I have wondered this for a very long time and probably thought about it for longer than I should have but the more I think about it, the more I seem to be correct and the more frustrating it is to talk to people about it...

Anyways, I'm sure everyone has heard of the saying "lefty loosy, right tighty" and that it usually comes up in conversation when tightening/loosening something around the house. Anyways, for the life of me, I cannot comprehend how this can work at all. Basically you are converting a 2 dimensional rotation into 1 dimensional motion. Given the correct scenario I can understand how this may seem to work (at least for half of a rotation) but it completely blows up during the second half of the rotation. This is how I think of it.

Just using the screw/screwdriver scenario, if you imagine that you start with the screwdriver bound to a screw with a little black mark on the head of the screw driver in the 12 o'clock "initial" position. With your hand, you start to turn the screwdriver so the black mark rotates in the clock-wise position until it hits the 3 o'clock position (1/4 turn). This logically seems like it is going in the "right" direction as the dot on the screwdriver moved closer to the "right" side of the room. Moving the screwdriver another 1/4 turn to the 6 o'clock position however moves this black dot away from the right side and thus it moves closer to the left side (relative to the 3 o'clock position). If you do this 2 more times, obviously you start back where you were thus 1/2 of the time you were moving to the "right" and 1/2 of the time you were moving to the "left".

The scenario probably was not necessary as I imagine you all have a very solid understanding of turning a facet handle, or screwing in a screw, but I just wanted to make sure...Regardless, I have pretty much given up on trying to tell this to other people as they generally just blow this off without even thinking about it and say something to the effect "well, everyone says this so I doubt it's wrong...". So please, if anyone can educate me on either a.why I am wrong and why this actually does work, or b.give me a better way to explain it to people so they actually believe me, I would be very much appreciative.

On a side note, I'd rather not have to just use the scenario where 2 people on opposites sides of a glass floor are watching something turn and thus each person see's either counter-clockwise or clockwise thus giving a left/right turn appearance depending on location. I feel there is a better way of explaining it than that, I just haven't come up with it yet...

I know this is somewhat sad but it is so frustrating to me when I hear people say this as I quickly rebuke with my answer that a 2d rotation cannot/should not be turned into a 1 d motion. Also, I consider myself fairly well educated (in 2nd year of medical school) with a few semesters of physics back in undergrad so if this does involve some complicated concepts/equations to adequately prove it, I feel I should be able to at the very least learn it without too much trouble. Thank you very very much for your thoughts!

Welcome to the PF.

I only read the start of your post, but just think of "top of the steering wheel". Just as moving the top of the steering wheel of your car steers the car to the right and left, that's the same kind of thing that the "righty tighty" advice is about. The rotating thing has to have a logical top and bottom for you to use this, so that is where the extra dimensionality comes from.

 

[melkor]

Welcome to the PF.

I only read the start of your post, but just think of "top of the steering wheel". Just as moving the top of the steering wheel of your car steers the car to the right and left, that's the same kind of thing that the "righty tighty" advice is about. The rotating thing has to have a logical top and bottom for you to use this, so that is where the extra dimensionality comes from.

Thanks for the welcoming and for the very quick reply. Also, please don't be offended by any of my answers/future answers. They are not meant to be offensive, I just don't have the time to write them as eloquently as I should right now.

I can see that if you consider a definite top/bottom then you can have the 2nd dimension but as far as the car scenario goes, I don't think that is a valid argument as you may turn the steering wheel more than 1/4 of a turn, but the wheels generally won't turn more than 90 degrees. If you were somehow able to keep turning the steering wheel so the wheels would go all the way around (which I don't think is even possible to imagine as the axle would just snap...), I don't think that argument would hold up. I have thought about the car example as that is what most people bring up it seems but you really are only getting a 1/4 turn effect even though you turn the steering wheel more. Again, I don't really know how to prove it one way or another, its just what my "gut" is telling me.

Anyways, I'm not trying to be difficult (although I feel I am, and am apologetic for it) and again am probably being more direct than I should, but I think my ocd has the best of me and this question has been driving me nuts for the past few hours today.

 

[K^2]

Because rotation is a 1-dimensional motion. It looks as if you have two degrees of freedom, say x and y, but in reality there is only one, because you have a constraint x²+y²=R². Due to that constraint, you really only have one degree of freedom, which is the angle. And if you have a screw with a fixed step, the angular position of the screw is proportional to the longitudinal position (say, along z).

 

[melkor]

Because rotation is a 1-dimensional motion. It looks as if you have two degrees of freedom, say x and y, but in reality there is only one, because you have a constraint x²+y²=R². Due to that constraint, you really only have one degree of freedom, which is the angle. And if you have a screw with a fixed step, the angular position of the screw is proportional to the longitudinal position (say, along z).

That is the kind of answer I was looking for!-at least for the first half. I definitely understand your reasoning with the angle giving you 1 dimension. I think I can somewhat understand the next 2 sentences, at least with how the angular position gives you 1 dimension, but I guess I am only convinced that that answers 1 of the problems.

Now that it is only a 1 dimensional object, how does that change the fact that half the time you are turning to the left, and the other half of the time you are turning to the right. (ie. every 1/4 turn it changes direction from left/right or right/left). Really really appreciate your guy's thoughts.

 

[Drakkith]

I assume that the vector is just reversed? (Not sure if its the correct terminology.)
Just like we have 3 spatial dimensions, but 2 opposite vectors for each one.