# Door naturally swings if the hinges are not properly aligned

#### Cyrus

I like it if someone could show me why a door naturally swings if the hinges are not properly aligned. Im not sure, but it might have been when a door is hanging on only one hinge that it naturally swings.

Thank you.

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#### HallsofIvy

Homework Helper
If the hinges are not "properly" aligned, one is not directly above the other. That means that the gravitational force on the door will not align with the hinges and will cause a torque about them.

#### Cyrus

heh, I just took appart one of the doors in my house and let it on one hinge. I realized that it DOES rotate, but that is because the hinge is TERRIBLE at preventing a moment. If it were a good hinge, in theory it would work. Kinda nice to be able to physically try a question out that you have and get an immediate anwser. Good thing I did not tear appart the wood where I left door hanging by that one hinge! .

In order for the door to move, it must have a moment produced that is in the verticle direction. (either up or down depending on the direction of rotation.)
But it seems this can only happen if the force has some component along the horizontal direction, and distance d from the location of the force to the axis of the door hinges.The weight acts only in the -k direction. So whats the horizontal force producing this moment?

I provided a picture. You can see that the weight acts down. And I broke it down into a force vector parallel to the axis of the hinges and one perpendicular. But I dont see how any of this can causes rotatation of the door since all forces act on the same plane as the door. So how is rotation orthagonal to this plane occuring?

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#### Cyrus

Im starting to belive that the door moving on its own is a bunch of crap. I took appart the door (for the second time). I removed the middle hinge. I left the top hinge alone, and I shimmed the bottom hinge about 1/4 of an inch. When the door is closed it wont slide into the frame. That should be MORE than enough to see some if any movement of the door on its own. I sat there........nothing happened. So I took some weights and added about 9lbs to the door thinking it might be too light........still nothing happens. I tried pushing the door to overcome static friction.........still nothing happens. I tried to think of it in terms of force vectors, ...........still could not find a logical reason to make the door swing on its own, there is no force anywhere perpendicular to the plane of the door and hinges to produce a moment that will allow the door to turn on its own. I searched the web for an anwser and found nothing. Was my premise that it does move on its own wrong from the very beginning!?

Damn.....something does make it move, because as I got something from my car, the door closed on its own, and my driveway is flat!

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#### Cyrus

Ah, I think I got it!

#### Cyrus

Ah, I think I got it!

It does not matter if the door is misaligned as seen from the big square side.
But if you look at it edge on, then it changes the whole picture. The weight vector points straight down reguardless. If the door is off center from the edge view, so that one hinge lies in or out more than the other, then we can break the weight down into a force parallel and a force perpendicular to the door. the perpeinduclar component acts, duh perpendicular to the hinges. This is not to say that the hinges cant prevent this force, they can, but the trick is they cannot prevent this MOMENT. Becuase its a 3d picture, you have to realize the weight acts at the centroid, which is 1/2 the width of the door. The hinge can do nothing to stop this moment, and so in this case, the door swings to the RIGHT. This is why my expeirment gave me no response when I Fooled with the hinges.

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#### Cyrus

does anyone agree/disagree?

Arg, that doesnt seem to work either. I moved the hing of the door out like in the picture and nothing happened. I even added 46lbs to the door and STILL no movement, even when nudged! I dont know anymore.

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#### shyboy

I think door will move if it's center of gravity can go down. If frame is inclined, the door will rotate for sure

#### shyboy

The door should rotate in your last picture, unless it is misaligned so much that there is a big friction in the hinges.

#### Cyrus

But when I tried misaligning the doors myself, it wouldent move. Thats after the fact that I added weight to increase the component of weight that causes the moment AND I nudged it to overcome static friction.

#### sreenathb

i think the door will not move on its own unless there is some amount of wind to push it.shyboy said that it will move provided the centre of gravity moves down as it rotates.such a situation is called an unstable equilibrium....ie just a little push is required is needed to get it moving and once u give it a small velocity it goes on unless it gets into a stable position.

#### Cyrus

There are doors that do move on their own though. I.e old heavy doors that shut on their own when left open. Im interested in seeking an anwser as to how they do this. Its not unstable equilibrium, because the door moves automatically. That means some component of the weight is causing the motion.

#### ehild

Homework Helper
cyrusabdollahi said:
There are doors that do move on their own though. I.e old heavy doors that shut on their own when left open. Im interested in seeking an anwser as to how they do this. Its not unstable equilibrium, because the door moves automatically. That means some component of the weight is causing the motion.
I've made a "door" from a knitting needle, a plastic cover of margarin and a bead shown in the picture. The needle represent the hinges of the door.
Keep the needle vertical: the door is in indifferent equilibrium.
Keep the needle horizontal: the door turns into vertical position, where its centre of mass is deepest.
Tilt the needle only a bit with respect to the vertical. The door has got a stable equilibrium position. If you move it away (open the door) the CM rises. The door will turn back to the original position if you release it as its weight has a component perpendicular to the plane of the door. This component has a nonzero torque in the direction of the possible axis of rotation (the needle).

ehild

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