Defining "freely hinged" for mechanics

Hello,
Could someone please clarify what "freely hinged" means in this context? Does this mean that there's a force/torque at point A, or can this be ignored?

As for the question itself, I took the moments about point A and then want to try and find the moments about C, but I'm not too sure what happens at point A.

Thank you! Equilibrium question.png

Reply 1

ghostwalker

17

Original post by dyuunn

Hello,
Could someone please clarify what "freely hinged" means in this context? Does this mean that there's a force/torque at point A, or can this be ignored?

As for the question itself, I took the moments about point A and then want to try and find the moments about C, but I'm not too sure what happens at point A.

Thank you!

Freely hinged means that the rods, individually, are free to rotate about the point, and that there are no frictional forces preventing that, i.e. no resistance to such a motion from the hinge.

At A, since it's not moving, the net force acting at A is zero.

Reply 2

dyuunn

OP

1

Original post by ghostwalker

Freely hinged means that the rods, individually, are free to rotate about the point, and that there are no frictional forces preventing that, i.e. no resistance to such a motion from the hinge.

At A, since it's not moving, the net force acting at A is zero.

Thank you for the answer - however, I'm still a little bit confused. If the rods are individually free to move, then does that mean that each rod is in a separate 'system'? If they are not connected, then how can I still take moment about C using forces from B? This equilibrium topic is really confusing for me... sorry :frown:

Reply 3

ghostwalker

17

Original post by dyuunn

Thank you for the answer - however, I'm still a little bit confused. If the rods are individually free to move, then does that mean that each rod is in a separate 'system'? If they are not connected, then how can I still take moment about C using forces from B? This equilibrium topic is really confusing for me... sorry :frown:

This is not the most basic of questions, so don't worry if you're struggling with it.

Alternative meaning: Freely hinged just means that there is no turning couple due to the hinge.

The rods are connected.

You can treat the rods individually, or both together as one item (since the parts aren't moving), depending on what you're trying to work out.

Treating them as one item, you can take moments about C and include the forces acting on B.

Reply 4

dyuunn

OP

1

Original post by ghostwalker

This is not the most basic of questions, so don't worry if you're struggling with it.

Alternative meaning: Freely hinged just means that there is no turning couple due to the hinge.

The rods are connected.

You can treat the rods individually, or both together as one item (since the parts aren't moving), depending on what you're trying to work out.

Treating them as one item, you can take moments about C and include the forces acting on B.

Okay, so there is no force acting about A (the freely hinged point), and therefore I can ignore it? If I'm wrong please correct me :frown:

In what situations would 'hinged' points exert some force on the system? There are questions that describe a rod as being hinged to the ground / wall surface, rather than another rod - in this instance, am I correct in saying that there would be force/moment on the rod due to the hinged contact?

Also, is it possible to take moments about a point outside an object and equate this to zero, if the object is said to be in equilibrium?

Sorry for burdening you with so many questions..

Thank you once again.

Reply 5

dyuunn

OP

1

Wait - no I must be wrong. There has to be some force at A, otherwise there is nothing holding up AB, is there?

(edited 7 years ago)

Reply 6

In One Ear

18

Original post by dyuunn

Wait - no I must be wrong. There has to be some force at A, otherwise there is nothing holding up AB, is there?

There is no net force at A, but there are definitely two equal in magnitude forces cancelling out to provide no motion.

Reply 7

dyuunn

OP

1

Original post by In One Ear

There is no net force at A, but there are definitely two equal in magnitude forces cancelling out to provide no motion.

Could you please tell me what causes these two forces and in which directions these forces might act?

Thank you.

Reply 8

ghostwalker

17

Original post by dyuunn

Okay, so there is no force acting about A (the freely hinged point), and therefore I can ignore it? If I'm wrong please correct me :frown:

A hinge allows rotational movement, and offers no resistive force to that, hence "freely hinged". It does prevent lateral movement and as such allows forces to be transmitted from one object to another if they are trying to move laterally.

If you treat both rods as one item, these forces at the hinge are internal to the item, and cancel themselves out, so you can ignore them.

Only if you treat the rods individually do you need to consider them as the forces would then be external. I don't recommend this method in this case, but if you want to, assign a vertical and horizontal component to the forces at A acting on AB, these will be equal and opposite to the forces acting on AC at A, and proceed from there - resolving vertically, horizontall, and taking moments as necessary for each rod.

In what situations would 'hinged' points exert some force on the system? There are questions that describe a rod as being hinged to the ground / wall surface, rather than another rod - in this instance, am I correct in saying that there would be force/moment on the rod due to the hinged contact?

Yes.

Also, is it possible to take moments about a point outside an object and equate this to zero, if the object is said to be in equilibrium?

Yes, but I've not seen it used at A-level. We usually choose a point in the object where at least one of the forces is acting - this reduces the amound of calculation and can eliminate unknown variables - depending on the question.

(edited 7 years ago)

Reply 9

dyuunn

OP

1

Thank you so much - that cleared up all the confusion!!

Defining "freely hinged" for mechanics

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