# Normal Force between two concentric cylinders

• Joshua Smith
In summary: If there is friction then the force will be reduced and the moment will be larger.You have assumed the normal force would continue to act along the same radius. If there is friction then the force will be reduced and the moment will be larger.
Joshua Smith

## Homework Statement

a cylinder sits inside of another fixed cylinder without friction and an internal force acts on the cylinder as shown in the diagram. Draw the normal force vector and write down the force and moment equations.

I drew in my normal vector to counteract the A force vector and wrote out the force and moment balance equations but when I did a check by plugging in numbers I got that the normal force causes a moment on the inner cylinder. What did I do wrong here?

## Homework Equations

Force balance, moment balance

In the picture the black dash is the thin outer cylinder

## The Attempt at a Solution

∑Fx = 0, ∑Fy = Ay - Ny = 0, ∑Fz = Az - Nz = 0,
∑Mx = (Az * you - Ay * za) + (Nz * r cosθ - Ny * r sinθ) = 0,
∑Mx = ( -Ay * za) + (Nz * r cosθ - Ny * r sinθ) = 0,

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A normal force is one that is perpendicular to the plane of contact between two bodies. In this case it would be radial to the cylinders.

Joshua Smith
haruspex said:
A normal force is one that is perpendicular to the plane of contact between two bodies. In this case it would be radial to the cylinders.

so In that case it doesn't matter where the A force originate, just its angle? it would like this then?

Joshua Smith said:
so In that case it doesn't matter where the A force originate, just its angle? it would like this then?
View attachment 112026
Yes, that's better.
There is a a mistake n the relevant equations you posted. They made a certain assumption which might not apply here.

Last edited:
haruspex said:
Yes, that's better.
There is a a mistake n the three relevant equations you posted. They all made a certain assumption which might not apply here.

since the outer cylinder is fixed the inner cylinder can't move so the forces should sum to zero, but it could rotate about x

Joshua Smith said:
since the outer cylinder is fixed the inner cylinder can't move so the forces should sum to zero, but it could rotate about x
Right.
So what equations do you now have?

haruspex said:
Right.
So what equations do you now have?

There will be a moment about the x-axis caused by the y component of the A force

∑Fx = 0, ∑Fy = Ay - Ny = 0, ∑Fz = Az - Nz = 0,
∑Mx = -Ay * za = 0

Joshua Smith said:
There will be a moment about the x-axis caused by the y component of the A force
Yes, so why did you write this:

Joshua Smith said:
∑Mx = -Ay * za = 0
?

For the linear forces, you need to get the x and y components of A in terms of A, θ, az and r.

haruspex said:
Yes, so why did you write this:

?

For the linear forces, you need to get the x and y components of A in terms of A, θ, az and r.
oops. I copy pasted and modified which led to me forgetting to take out the = 0.

I have a question about this with friction. If you added friction between the two cylinders then there would be a tangential force acting at the point where the normal force touches to counteract the rolling of the cylinder but then the force balance wouldn't work out? How is this rectified?
∑Fn = A - N = 0, ∑Ft = -uN ~= 0,
∑Mx = -Ay * za + uN * r

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Joshua Smith said:
then the force balance wouldn't work out
You have assumed the normal force would continue to act along the same radius.

## 1. What is the definition of normal force between two concentric cylinders?

The normal force between two concentric cylinders is the force exerted by one cylinder on the other in a direction perpendicular to their surfaces. This force arises due to the pressure difference between the two cylinders.

## 2. What factors affect the magnitude of normal force between two concentric cylinders?

The magnitude of normal force between two concentric cylinders is affected by the radius of the cylinders, the pressure difference between them, and the coefficient of friction between their surfaces. Additionally, the material and surface roughness of the cylinders can also influence the normal force.

## 3. How is the normal force between two concentric cylinders calculated?

The normal force between two concentric cylinders can be calculated using the equation F = P * A, where F is the normal force, P is the pressure difference, and A is the area of contact between the cylinders. This equation assumes that there is no friction between the two cylinders.

## 4. What is the direction of normal force between two concentric cylinders?

The direction of normal force between two concentric cylinders is always perpendicular to the surfaces of the cylinders. This means that the force is directed towards the center of the smaller cylinder.

## 5. How does the normal force between two concentric cylinders affect their motion?

The normal force between two concentric cylinders is a balancing force that prevents the cylinders from moving towards or away from each other. It also plays a role in the rolling motion of the cylinders, as it helps to maintain their circular shape and prevent slipping between their surfaces.

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