# Static rotational friction: does diameter matter?

• I
• ShearStress
In summary, the question is whether the diameter of a washer in a bolted joint affects the static friction on the surface. There are two ways to view this: either the diameter doesn't matter because friction is not affected by surface area, or the larger the diameter, the higher the moment due to the increased distance from the axis of rotation. The solution is to determine if the joint slips linearly or if the bolt is tightened using torque, and then calculate the torque using the average diameter of the slipping surfaces. This information is typically found in books on machine design.
ShearStress
Imagine a bolted joint with a washer between the bolt and the surface.

Assuming the washer is always covered by the bolt head so it's getting a consistent load, does the washer's diameter impact the static friction being imparted on the surface?

I see two conflicting ways of viewing this:
1.) Friction doesn't care about surface area, so no the washer diameter doesn't matter (perhaps this is more relevant for linear friction, not rotational?)
2.) The larger the washer is, the higher the moment is since the friction is acting further from the axis of rotation

What's the answer and how can this solution be expressed mathematically?

I don't see a conflict, the friction force stays the same but the moment is proportional to the diameter (assuming the normal force is equally distributed along the washer's diameter, which is not certain).

1) If you are asking about the force to make the joint slip linearly, then your statement #1 is correct.

2) If you are asking about the torque to tighten the bolt, then your statement #2 is correct. The procedure is:
A) Determine if the bolt head is slipping on the washer or the washer is slipping on the joint.
B) Calculate the torque using the average diameter of the slipping surfaces, assuming the compressive stress is evenly distributed.

A quick search for bolt torque calculations did not find this, but it is in any book on machine design. It's in the chapter on bolted joints.

## 1. What is static rotational friction?

Static rotational friction is the force that resists the movement of an object around an axis. It occurs when there is no relative motion between the object and the surface it is in contact with.

## 2. How does static rotational friction differ from kinetic rotational friction?

Static rotational friction occurs when there is no relative motion between the object and the surface, while kinetic rotational friction occurs when there is relative motion between the two. In other words, static friction prevents an object from rotating, while kinetic friction slows down the rotation of an object.

## 3. Does the diameter of an object affect static rotational friction?

Yes, the diameter of an object does affect static rotational friction. The larger the diameter, the greater the moment of inertia, which results in a greater resistance to rotational motion. This means that a larger diameter object will experience a higher static rotational friction force than a smaller diameter object.

## 4. How does the surface material affect static rotational friction?

The surface material can have a significant impact on static rotational friction. Rougher surfaces tend to have higher coefficients of friction, resulting in a greater resistance to rotational motion. Smooth surfaces, on the other hand, have lower coefficients of friction and therefore experience less static rotational friction.

## 5. Can static rotational friction be reduced?

Yes, static rotational friction can be reduced by using lubricants, such as oil or grease, between the object and the surface. Lubricants reduce the coefficient of friction between the two surfaces, making it easier for the object to rotate. Additionally, using smoother surfaces or reducing the weight of the object can also help reduce static rotational friction.

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