# What makes a door move, the torque or the force or both?

• alkaspeltzar

#### alkaspeltzar

I have seen an example of a horizontal beam on a hinge. Beam of length L acted on my gravity MG at center, where the hinge supplies 1/4MG force to the door. Therefore there is a net torque, causing angular acceleration and a net force, causing translation about the center of mass.

Maybe it is because many examples focus only on the torque, but i read examples where they only look at the torque on a interior house door say a person pushes it. But if i am not mistaken when we push a door, similar to the beam, there is both torque and force which is why it moves? Without some force, it would have no torque, but it need a force to move its center of mass as well.

Maybe i have taken the force at the hinge point for granted, as with wheels and gears, it is equal to the applied force, so it creates no torque and it can safely be ignored.

Attached is an example of what i reading and applying to the door.

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How do have torque without force?

Try to open a door by applying a force at the hinges. If the door opens, it's the force that opens it. If the door doesn't open it's the torque. Why do you think door manufacturers routinely (and cleverly) place door handles where they do?

Dale
Try to open a door by applying a force at the hinges. If the door opens, it's the force that opens it. If the door doesn't open it's the torque. Why do you think door manufacturers routinely (and cleverly) place door handles where they do?

No, i guess my question was i thought the door only had a net torque, no net force. I thought the hinge supplied an equal force to the applied force, so there was only torque doing the work

How do have torque without force?

Not arguing that. I just thought the door would have no net force. I thought the hinge would supply equal and opposite force, so it was the torque only. But i see that is not true.

There is both a net force and net torque that get it moving correct?

So from what i understand, since this is not a wheel or gear where the system is balance by an equal force from an axle so the CofMass doesn't move, there has to be BOTH net force and net torque to make a door swing correct?

No, i guess my question was i thought the door only had a net torque, no net force. I thought the hinge supplied an equal force to the applied force, so there was only torque doing the work
Possibly you need to consider the distinction between a revolving door and one which is hinged on the side.

Does the center of mass of the revolving door move when the door is used?
Does the center of mass of the hinged door move when the door is used?

Pick an axis about which to compute angular momentum.
Does the angular momentum of the revolving door change when it is used?
Does the angular momentum of the hinged door change when it is used?

alkaspeltzar
Possibly you need to consider the distinction between a revolving door and one which is hinged on the side.

Does the center of mass of the revolving door move when the door is used? no
Does the center of mass of the hinged door move when the door is used? yes

Pick an axis about which to compute angular momentum.
Does the angular momentum of the revolving door change when it is used? yes
Does the angular momentum of the hinged door change when it is used? yes

So becuase there is both change in angular moment and the c of mass moves in the door hinged(not revolving around a center), there is both net force and torque correct? I feel like i didnt think about it before which is why it is odd. So please let me know

DaveE and jbriggs444
So becuase there is both change in angular moment and the c of mass moves in the door hinged(not revolving around a center), there is both net force and torque correct?
Yes. That is the correct conclusion that you should draw.

alkaspeltzar
So from what i understand, since this is not a wheel or gear where the system is balance by an equal force from an axle so the CofMass doesn't move, there has to be BOTH net force and net torque to make a door swing correct?
"Move" is not a good word choice. If the CoM accelerates, there has to be a net force acting on it and you can always pick a point in space about which there will be a net torque.

"Move" is not a good word choice. If the CoM accelerates, there has to be a net force acting on it and you can always pick a point in space about which there will be a net torque.

Yes, you are right. but i was trying to define the problems such that it was understood there are both types of motion. Rotational about the pivot but still translation thru the center of mass. So in this case, we have a force pushing the door forward but due to the fixed hinge, it is also causing a torque/rotation about the hinge.

Yes. That is the correct conclusion that you should draw.
why do i feel like in many problems we ignore the hinge force or even the net force on the door, only caring about the torque? Is this because we can figure out how fast the door swings and such without it, so it is not necessary? IF we know the force to the door, we can run the torque calc to determine what torque makes it swing. The fact there is a net force is true, but not helpful in understanding its motion.

Or is it because in many torque examples, say a wrench and a bolt, we only care about the torque on the bolt, and what happens to the wrench is just extra?

why do i feel like in many problems we ignore the hinge force or even the net force on the door, only caring about the torque?
If we have a clear and easy way to solve a problem, we can use that approach and ignore all of the other ways, regardless of how clear and easy the alternatives might be.

If we can figure out how fast a door opens using an argument based on torque then we need not bother ourselves by summing linear forces to determine how the center of mass moves. We already know how the center of mass must move.

Lagrangian mechanics is something that I have never fully comprehended, but my understanding is that it provides an entirely different perspective on constraint forces (e.g. hinge forces) in problem solving.

russ_watters and alkaspeltzar
So isn't it both the torque and force applied to the door making it move?
You hand makes the door move. Torque and force are quantities used compute how it will move.

nasu and alkaspeltzar
why do i feel like in many problems we ignore the hinge force or even the net force on the door, only caring about the torque?
A hinge is a device which is designed to provide any arbitrary force but zero torque (about the hinge). You only care about the torque because the hinge force can be whatever it needs to be to satisfy the motion determined by the torque.

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alkaspeltzar
Or is it because in many torque examples, say a wrench and a bolt, we only care about the torque on the bolt, and what happens to the wrench is just extra?
The Force that's applied to a wrench will be in a particular direction and very little actual Torque will be applied by your hand unless the wrench is held like a screwdriver. Also, the effect of this force may just move a light workpiece across the bench without turning it at all. Trying to classify what's "really going on" and give it a name is really a bit futile. Force and Torque are both at work in most situations.

If you are ever lucky enough to have a space flight, observe what happens to free objects when you push and pull them. Failing that, try working with a heavy boat and manoeuvring it against another boat. You soon realize that you 'can' apply torque by gripping a rail with both hands but the result is often surprising.

The Force that's applied to a wrench will be in a particular direction and very little actual Torque will be applied by your hand unless the wrench is held like a screwdriver.
Not sure what you mean, the bolt would receive a lot of torque from the wrench/hand.

But I do agree, torque and force go hand in hand in most applications

A hinge is a device which is designed to provide any arbitrary force but zero torque. You only care about the torque because the hinge force can be whatever it needs to be to satisfy the motion determined by the torque.
This makes a lot of sense. The hinge helps provide centripetal force to maintain rotation and create the tangential forces on the center of mass so it moves both rotationally and translationally equally.

Makes a lot of sense then why torque is of the main concern

A hinge is a device which is designed to provide any arbitrary force but zero torque (about the hinge). You only care about the torque because the hinge force can be whatever it needs to be to satisfy the motion determined by the torque.
Pretty sure someone told me this once. I think this was missing in my understanding. Torque creates the rotation and the hinge/pivot causes the rest to balance.

Dale
Yes, you are right. but i was trying to define the problems such that it was understood there are both types of motion.
Fair enough, but the question you‘re asking is not ‘What makes a door move?” but rather “What makes a door start moving?”. The latter implies changes in momentum and angular momentum, which is what torques and forces do.

isn't torque defined in terms of force? as in if there's no force, then there's no torque, right?

isn't torque defined in terms of force? as in if there's no force, then there's no torque, right?
Consider the examples of revolving door then.
If you push one side of revolving door and simultaneously pull the opposite side of revolving door with opposite and equal force then there are gross forces causing torque on the door - but there is no net force on door, and therefore no net force on pivot.
Now suppose you just push the door at one point which is the centre of mass of the door leaf.
There will be no torque if there are no hinge forces - for example the hinges are broken so the push turns out to push the door out of the frame rather than turn the door.
Assume the hinges hold. Then does the door translate?
If you push a leaf of the revolving door, the opposite leaf will be moving in opposite direction, so the door does not translate. It means there must be no net force on the door - the push on one leaf must be balanced by equal and opposite hinge forces if you do not balance it by equal and opposite pull.
If the door, however, has one leaf then the fact that it turns shows that there are hinge forces - but the fact that the door translates shows that the hinge forces must not be equal to the push.

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alkaspeltzar and Lnewqban
Not sure what you mean,
You can't apply a torque without impressing two forces. You arm can do that (to a small extent) by 'twisting'. Otherwise, you use another (reaction) force and the distance between the forces governs the resulting torque.
By applying a torque, you can ensure that there is no net linear acceleration. You can't ensure that with a simple pull / push on a wrench handle.

alkaspeltzar
if there's no force, then there's no torque, right?
If there's only one force there's no torque.
Why are we chasing our tails without drawing any diagrams?

Consider the examples of revolving door then.
If you push one side of revolving door and simultaneously pull the opposite side of revolving door with opposite and equal force then there are gross forces causing torque on the door - but there is no net force on door, and therefore no net force on pivot.
Now suppose you just push the door at one point which is the centre of mass of the door leaf.
There will be no torque if there are no hinge forces - for example the hinges are broken so the push turns out to push the door out of the frame rather than turn the door.
Assume the hinges hold. Then does the door translate?
If you push a leaf of the revolving door, the opposite leaf will be moving in opposite direction, so the door does not translate. It means there must be no net force on the door - the push on one leaf must be balanced by equal and opposite hinge forces if you do not balance it by equal and opposite pull.
If the door, however, has one leaf then the fact that it turns shows that there are hinge forces - but the fact that the door translates shows that the hinge forces must not be equal to the push.
So given one leaf door, there are both force and torque on the door, as it turns and translates. Is that correct?

With revolving door, there is only rotation therefore no net force

Dale
isn't torque defined in terms of force? as in if there's no force, then there's no torque, right?
Torque is indeed defined in terms of force, but we can have torque even when there is no net force. An example might be spinning a wheel on a shaft by placing my hands on opposite sides of the wheel and pushing with one hand, pulling with other. The center of mass of the wheel stays put so we know that there's no net force on the wheel, but it starts to spin telling us that there is a net torque on the wheel.
If there's only one force there's no torque.
Even when there is only one force there's still torque (in general - we can always choose a point about which to calculate the torque in such a way that it comes out zero). If there is only one force involved then the net force is necessarily non-zero and the center of mass will accelerate along with any rotation caused by the torque

alkaspeltzar
Torque is indeed defined in terms of force, but we can have torque even when there is no net force. An example might be spinning a wheel on a shaft by placing my hands on opposite sides of the wheel and pushing with one hand, pulling with other. The center of mass of the wheel stays put so we know that there's no net force on the wheel, but it starts to spin telling us that there is a net torque on the wheel.
Even when there is only one force there's still torque (in general - we can always choose a point about which to calculate the torque in such a way that it comes out zero). If there is only one force involved then the net force is necessarily non-zero and the center of mass will accelerate along with any rotation caused by the torque
Can you confirm my question please. Thanks

So given one leaf door, there are both force and torque on the door, as it turns and translates. Is that correct?

With revolving door, there is only rotation therefore no net force
http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html

Imagine a very wide hinge-less door floating out in space, which you are pushing while being supported by a massive object, like the International Space Station.
The closer to the center of mass of that door that your hand perpendicularly pushes it, the closer to a pure translation movement you induce.
As the pushing area is relocated more and more towards one of the edges of the door, the movement that you induce is more a rotation than a translation.

alkaspeltzar
Can you confirm my question please. Thanks
You mean the question in the title of the thread?

For an ordinary swinging door, the kind that is hinged at one side: Force causes the center of mass of the door to move, torque causes the door to rotate on its hinges.

For a revolving door: the center of mass doesn’t moveso there is no net force on the door. There is a torque, and that’s what causes it to revolve.

alkaspeltzar
So given one leaf door, there are both force and torque on the door, as it turns and translates. Is that correct?
You need neither force nor torque to turn and translate. You need them only to change the rate of turning and translating.

alkaspeltzar
You need neither force nor torque to turn and translate. You need them only to change the rate of turning and translating.
This is true, and throughout the entire thread just about everyone (including myself, in the posts just above) has been saying “move” when “start moving” would be more accurate.

There is much to love about the English language, but it is not a precision instrument when used naturally.

sophiecentaur and russ_watters
You mean the question in the title of the thread?

For an ordinary swinging door, the kind that is hinged at one side: Force causes the center of mass of the door to move, torque causes the door to rotate on its hinges.

For a revolving door: the center of mass doesn’t moveso there is no net force on the door. There is a torque, and that’s what causes it to revolve.
Yes this question. But you have answered it. I guess for many years i have not thought about the force on the center of mass, just assume it was torque. Learn something every day

So given one leaf door, there are both force and torque on the door, as it turns and translates. Is that correct?

With revolving door, there is only rotation therefore no net force

This is true, and throughout the entire thread just about everyone (including myself, in the posts just above) has been saying “move” when “start moving” would be more accurate.

There is much to love about the English language, but it is not a precision instrument when used naturally.
i think everyone knew what i meant, this is not english forums LOL

http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html

Imagine a very wide hinge-less door floating out in space, which you are pushing while being supported by a massive object, like the International Space Station.
The closer to the center of mass of that door that your hand perpendicularly pushes it, the closer to a pure translation movement you induce.
As the pushing area is relocated more and more towards one of the edges of the door, the movement that you induce is more a rotation than a translation.

In the link, it shows for a point mass the different is null, you can explain the motion either thru torque or thru force, as one induces the other.

Same for the door and your space example. The door would have both rotation and translation, so hence the force moves it forward and causes torque.

Lnewqban
you can explain the motion either thru torque or thru force, as one induces the other.
While this is always true, sometimes it is more difficult to know one or the other. In the case of a door with a hinge we know that the torque about the hinge provided by the forces at the hinge are zero. We do not know the forces at the hinge. So although the motion can be explained either way (in fact a full description requires both), it is much more simple to analyze the torque. From only the torque we can determine the full motion and thereby determine the unknown hinge force. But since the hinge force is unknown in advance it can only be used in this case as an "after the fact" explanation.

That is the reason why door questions and discussions focus on the torque only. Not because the forces are zero, but because they are unknown and adapt to whatever value is needed to satisfy the motion as determined by the torque.

russ_watters and alkaspeltzar