# Friction generating torque

• fobos3
In summary: Sorry. Right - torque. I was thinking about the normal force. (I'll try to be more careful in the future when switching the point of discussion like that.)In summary, the diagram is misleading as it implies that the normal force acts through the center of mass. However, in reality, the normal force shifts to exert a counter-torque when a force is applied at an angle to the center of mass. As the normal force redistributes on the bottom surface, gravity pulls through the center while the normal force does not. This can lead to a new equilibrium condition with a different distribution of normal force and friction force, allowing for the possibility of toppling if the applied

#### fobos3

http://en.wikipedia.org/wiki/File:Friction_alt.svg" [Broken]

Look at the picture. If the friction force acts as it is shown, it would create torque. The force $$\textbf{F}$$ acts at angle $$0^\circ$$ so it doesn't generate torque. A simple thought experiment shows that if this is true, then the cube would topple over as soon as we apply any force at the centre of mass (which is obviously wrong). Can you clarify this for me, please.

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The diagram is misleading as it implies that the normal force acts through the center of mass. But it doesn't. As you push with force F, the normal force shifts to exert a counter-torque.

I'm not sure I would call it misleading, but definitely a simplification. You'll note that it does not give any dimensions anywhere. That's an indication to you that you should ignore any implications of those dimensions - they aren't part of what is trying to be explained.

Perhaps it would be helpful in trying to avoid the confusion if they applied the force at the base of the square/box to eliminate the torque, but I wouldn't typically consider that necessary for the example to be useful.

 Meh - perhaps that isn't even necessary: a varying normal force due to the torque wouldn't change the basic form of the friction equation at all - you'd still integrate it to get a single normal force and the friction would remain unchanged.

fobos3 said:
A simple thought experiment shows that if this is true, then the cube would topple over as soon as we apply any force at the centre of mass (which is obviously wrong).

I think you are essentially correct, but in real life gravity would exert a stabilizing torque once the block starts to topple (as per DocAl's explanation). Under the right conditions, the stabilizing torque can be insufficient, and the block will actually topple. I just did a simple test pushing my coffee cup with my finger. I can push even below the center of gravity (but not at the base - as russ_watters says, this eliminates the torque) and still seem to see a toppling effect, if the friction is strong enough to keep the cup from sliding. My cup is very tall and narrow which tends to make the effect more noticeable since the moment arm for the gravity counter torque is smaller if the base is shorter.

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Ok, I get this. But when we apply a force at the top corrner the friction moves tocounter the torque. And the normal force acts at the centre of gravity. I don't understand when the normal force moves and when the friction force moves.

fobos3 said:
Ok, I get this. But when we apply a force at the top corrner the friction moves tocounter the torque. And the normal force acts at the centre of gravity. I don't understand when the normal force moves and when the friction force moves.

If I understand you correctly, I think russ_watters basically answered this in his last edit. The application of a force at the top corner induces a torque both from the applied force and from the reaction (friction force). Assuming that the force is not strong enough to topple the block, there will be a new equilibrium condition. The picture looks the same, but the distribution of the normal force and the friction force is no longer constant over the bottom surface. The far side of the block now has greater normal force and greater friction force. You can now think of the far bottom corner as a fulcrum about which the block wants to turn. It's easier to think about it if you consider the case where the near bottom corner actually comes off the ground. Then, the entire friction force and normal force is at the far bottom corner. Now you can see how gravity can create the counter torque. Gravity pulls the block down through the center of gravity, but the turning point is at the far bottom corner.

Wow, that sounds confusing, but I think it should give you the intuition you need.

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elect_eng said:
I think you are essentially correct, but in real life gravity would exert a stabilizing torque once the block starts to topple (as per DocAl's explanation).
Gravity acts at the center of mass, thus exerts no torque about the center of mass. But friction and the normal force do exert torques about the center of mass. (I know what you mean, but I'm trying to be precise.)

fobos3 said:
Ok, I get this. But when we apply a force at the top corrner the friction moves tocounter the torque.
The line of action of the friction force doesn't change, thus the torque it produces remains the same.
And the normal force acts at the centre of gravity. I don't understand when the normal force moves and when the friction force moves.
The normal force is a "reaction" force. It shifts to prevent acceleration, as best it can. (Just like when you push a wall, the wall pushes back--up to the point that it crumbles.) It does not simply act through the center of mass. That's why I said your diagram was misleading for understanding torques. (It's perfectly OK if all you care about is translational motion.)

Bottom line is you have to draw a free body diagram to see where, exactly, the forces and moments are and where they work. Ie, if the force pushing on the block is applied to the middle, it obviously can't apply a torque about the center of mass. If applied above or below the center of mass of the block, it can.

Doc Al said:
Gravity acts at the center of mass, thus exerts no torque about the center of mass. But friction and the normal force do exert torques about the center of mass. (I know what you mean, but I'm trying to be precise.)

Yes, I agree. Once you start pushing, the normal force redistributes on the bottom surface. So gravity pulls through the center, but normal force does not. But, I'm trying to create the intuitive explanation that the turning point for torque is not the center of gravity, but the far lower corner of the block. I think this only is strictly correct if the near bottom corner lifts off the ground, but at that point it's clear that gravity, acting through the center of gravity of the block, can create the counter torque. Hopefully, this mental picture makes the understanding easier.

russ_watters said:
Bottom line is you have to draw a free body diagram to see where, exactly, the forces and moments are and where they work.
Exactly. (The shifting line of action of the normal force is a subtle point not generally discussed in intro textbooks.)
Ie, if the force pushing on the block is applied to the middle, it obviously can't apply a torque about the center of mass.
Right, but the friction and normal force can certainly exert such torques.

elect_eng said:
Yes, I agree. Once you start pushing, the normal force redistributes on the bottom surface. So gravity pulls through the center, but normal force does not. But, I'm trying to create the intuitive explanation that the turning point for torque is not the center of gravity, but the far lower corner of the block. I think this only is strictly correct if the near bottom corner lifts off the ground, but at that point it's clear that gravity, acting through the center of gravity of the block, can create the counter torque. Hopefully, this mental picture makes the understanding easier.
Choosing the center of mass as the pivot point for calculating torque is always legitimate. Choosing the lower edge as the pivot is also perfectly fine, as long as the cube is not accelerating. (If it accelerates, the relationship between torques about the edge and the subsequent rotational acceleration is a bit more complicated.)

Since the diagram showed Ff = μN, I assume the block is moving (kinetic friction) and perhaps accelerating.

Doc Al said:
Choosing the center of mass as the pivot point for calculating torque is always legitimate. Choosing the lower edge as the pivot is also perfectly fine, as long as the cube is not accelerating. (If it accelerates, the relationship between torques about the edge and the subsequent rotational acceleration is a bit more complicated.)

Since the diagram showed Ff = μN, I assume the block is moving (kinetic friction) and perhaps accelerating.

I wasn't implying that it is not legitimate to choose the center of mass as the pivot point (i said intuitive explanation to mean not a strictly correct one). I'm just trying to give some type of explanation that the OP finds helpful. As you say, the lower edge as the pivot point is also perfectly fine, so with that thought, one can view gravity as inducing a stabilizing torque.

I'm not trying to argue about semantics or perfect explanations. I know the experts here can handle that. However, sometimes certain visualization ideas can help someone come to grips with a confusing concept.

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We sure know how to beat a topic into the ground, don't we?

Thanks for the replies. I've found it explained in the next chapter in my textbook (I'm studying for A-levels. This is before uni in the UK).

## 1. What is friction generating torque?

Friction generating torque is the force created by the resistance between two objects in contact that are moving relative to each other. This force can cause rotation and is often seen in machines and engines.

## 2. How is friction generating torque calculated?

The calculation of friction generating torque involves multiplying the coefficient of friction between the two surfaces by the normal force acting on the surfaces and the distance between the pivot point and the point where the force is applied.

## 3. What factors affect the amount of friction generating torque?

The amount of friction generating torque can be affected by the type of materials in contact, the roughness of the surfaces, the amount of force applied, and the speed at which the objects are moving relative to each other.

## 4. How does friction generating torque impact the efficiency of machines?

Friction generating torque can decrease the efficiency of machines by converting some of the input energy into heat, which is not useful for the intended purpose. This can also cause wear and tear on the machine parts, leading to decreased performance over time.

## 5. How can friction generating torque be reduced?

To reduce friction generating torque, lubricants can be used to reduce the resistance between surfaces. Additionally, smoother surfaces and proper maintenance can also help to decrease the amount of friction and torque produced.