# How the action-reaction principle works in the case of a screw fastener and a nut?

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A screw fastener advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?

According to my understanding, (a) justifies screw's motion (helical) and should be the answer, otherwise the screw wouldn't be able (due to screw threads) to advance into the nut.

Could someone help me understand the above? (a drawing would be very welcome!)

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jbriggs444
Homework Helper
A screw advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?

According to my understanding, (a) justifies screw's motion (helical) and should be the answer, otherwise the screw wouldn't be able (due to screw threads) to advance into the nut.

Could someone help me understand the above? (a drawing would be very welcome!)
You are trying to characterize a force that exists all up and down and around the threads of a screw and nut and treat it as if it were a single force applied in a single direction?

That's what vector sums are for.

I have a pet peeve about classifying forces as "action" and "reaction". Those are empty adjectives. They mean nothing.

sophiecentaur
Gold Member
2020 Award
Assuming there are no frictional forces (or negligible):
If there were no friction forces, all you'd be doing is giving the nut angular and linear acceleration. There will be a force / couple pushing the nut along / around and there will be a reaction force / couple against the wrench. This is exactly the same principle (it always is) at work when you push a block across a flat, horizontal and frictionless table.

As @jbriggs444 implies, first deal with your concerns about what's action and what's reaction (arbitrary choice really) then get to solving any problem with a Forces diagram.

@sophiecentaur,
Certainly, there has to be a wrench (or something else) to initiate nut's motion, however my question points to where the action-reaction pair appears between the male and female threads.

So, If I understood correctly from your answer, does what I marked as (a) is the correct answer?

jbriggs444
Homework Helper
If there is no friction, how would the force end up being tangential?

Just to make the question clearer for all of us: I just would like to know in terms of the action-reaction principle, if the nut has to go around the screw thread over an action force (tangential to helix trajectory) then in order this motion to occur is required a reaction (tangential to helix trajectory) force (a pushing back) on screw's thread. Is this correct?

Lnewqban
Gold Member
@sophiecentaur,
Certainly, there has to be a wrench (or something else) to initiate nut's motion, however my question points to where the action-reaction pair appears between the male and female threads.

So, If I understood correctly from your answer, does what I marked as (a) is the correct answer?
A screw-nut system is equivalent to an inclined plane wrapped around a cylinder.
It is still a simple machine to do work with.
Just replace the weight of the sliding block with axial load.
Friction is what prevents actual systems from unscrew themselves under axial load.

This is the case of your problem:
https://en.wikipedia.org/wiki/Inclined_plane#Frictionless_inclined_plane

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If there is no friction, how would the force end up being tangential?
I am speaking about an ideal situation where there are no energy losses due to friction. That was my initial thought.

jbriggs444
Homework Helper
I am speaking about an ideal situation where there are no energy losses due to friction. That was my initial thought.
The question remains. We have a bolt that is freely rotating as it advances into a nut. There is no friction. Why would you expect any tangential force? Why would you expect any force at all?

When you say "tangential", which direction is that? Along the helical track of a thread? Or around a circle at a fixed radius from the center line?

[In the U.S. dialect at least, the distinction between a "screw" and a "bolt" is that screws are self-threading. A "screw" does not use a nut. It cuts or squishes into the material (typically wood, plastic or sheet metal) making the threads with which it meshes. Bolts, by contrast use nuts or pre-threaded ("tapped") holes. This fact is reflected in the design attributes of the two fasteners. "Screws" tend to have pointed tips. "Bolts" tend to have flat tips.]

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The question remains. We have a bolt that is freely rotating as it advances into a nut. There is no friction. Why would you expect any tangential force? Why would you expect any force at all?

[The distinction between a "screw" and a "bolt" is that screws are self-threading. A "screw" does not use a nut. It cuts into the material (typically wood, plastic or sheet metal) making the threads with which it meshes. Bolts, by contrast use nuts or pre-threaded ("tapped") holes]
You are right, I messed it up a little. What I am speaking about is an ideal situation where there are no energy losses due to friction and we have a screw fastener and a nut. The initial thought was about a frictionless mechanical advantage. It sounds it contradicts in principle since the screw and the nut work based on frictional forces. Just for the sake of the argument we keep these frictional forces at play but without consuming energy. I just would like to know if what I share on Comment #6 is correct.

When you say "tangential", which direction is that? Along the track of a thread? Or around a circle at a fixed radius from the center line?
Along the track of the thread.

jbriggs444
Homework Helper
Along the track of the thread.
Then the absence of friction means the absence of tangential force.

Now you have to decide whether there is tension on the screw/bolt.

Then the absence of friction means the absence of tangential force.

Now you have to decide whether there is tension on the screw/bolt.
And with tension what is the result?

jbriggs444
Homework Helper
And with tension what is the result?
Still no tangential force. But what about the normal force?

Then what I wrote in Comment #6 should hold over the normal force or not? The nut has in a way to push the screw fastener (or vice versa) in order to advance. But the normal force would be perpendicular to the track of the thread, right?

jbriggs444
Homework Helper
Then what I wrote in Comment #6 should hold over the normal force or not? The nut has in a way to push the screw fastener (or vice versa) in order to advance. But the normal force would be perpendicular to the track of the thread, right?
Right. The normal force at any point along the thread is perpendicular to the track of the thread. It has a non-zero component parallel to the axis of the bolt.

Picture a bolt inserted through this spring and threaded into the nut.

If the normal force is perpendicular to the track of the thread then, how the nut may push the screw fastener (or vice versa) in order to advance? This is the reason what I shared on my first post that the action and reaction forces should tangential to the threads of the nut and the screw fastener. Otherwise, motion cannot occur.

jbriggs444
Homework Helper
If the normal force is perpendicular to the track of the thread then, how the nut may push the screw fastener (or vice versa) in order to advance? This is the reason what I shared on my first post that the action and reaction forces should tangential to the threads of the nut and the screw fastener. Otherwise, motion cannot occur.
Motion does not need force. Acceleration needs force. You provided the force to cause the initial acceleration when you started the bolt spinning. In the absence of friction and tension, that is all that is needed. The nut can spin onto the bolt indefinitely with no further force required.

Now we need to work through the consequences of tension and normal force.

Motion does not need force. Acceleration needs force.
In order the screw fastener to advance into the nut (with frictions but we assume they consume negligible energy), a continuous force is required. Stopping the action (or the wrench), the screw fastener will stop advancing. In this particular case force is associated with motion.

jbriggs444
Homework Helper
In order the screw fastener to advance into the nut (with frictions but we assume they consume negligible energy), a continuous force is required. Stopping the action (or the wrench), the screw fastener will stop advancing.
Either it is negligible energy and no force is required or it is non-negligible energy and a force is required.

Pick one. You cannot have it both ways.

Mark2020
OK, I pick the second one.

jbriggs444
Homework Helper
OK. So you have friction and you need a tangential force. So you need a wrench. What's the problem?

Mark2020
OK. So you have friction and you need a tangential force. So you need a wrench.
Does it mean what I write in Comment #6 is correct?

Dale
Mentor
2020 Award
A screw fastener advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?
I also am having a hard time wrapping my mind around a bolt and a nut without friction. So I will simply answer with regards to an ordinary bolt and nut that do have friction under normal fastening conditions.

The threads of the bolt and nut form a pair of inclined planes that are in contact all along their length. So you don't have a force per-se but rather a force density. The technical term is a stress. There are components of the stress directed perpendicular to the inclined plane surface and components of the stress directed parallel to the inclined plane section.

If you take an arbitrary section of the nut thread surface then you can integrate the stress over that section to get the force acting on that section of the nut thread surface. By Newton's third law there will be a corresponding section of the bolt thread surface, and if you integrate the stress over that section of the bolt thread surface then you will find that the force is equal and opposite the corresponding nut thread force.

I don't know how to translate that to a frictionless case, but there it is for the usual case.

Mark2020
jbriggs444
Homework Helper
Does it mean what I write in Comment #6 is correct?
Yes, the "action reaction principle" holds for every incremental section where screw thread contacts nut thread. The tangential/frictional force of the one on the other is equal and opposite to the tangential/frictional force of the other on the one.

In practical terms, this means that you need two wrenches. One to drive the screw and one to hold the nut.

Dale, hutchphd and Mark2020
jbriggs444