Why are the radial and the axial stress in a rotating thin ring null?

In summary, the radial stress in a rotating thin ring is null due to the balance of the centrifugal and radial forces in the circular shape of the ring. The axial stress is also null due to the perpendicular direction of these forces. However, external forces or a non-perfectly circular shape can cause non-null radial and axial stress. The speed of rotation does not directly affect the stress, but it can cause changes in the ring's shape and lead to non-uniform stress. The radial and axial stress are not always equal in magnitude due to these factors.
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Homework Statement
look at the image
Relevant Equations
centrifugal forces
Greetings, while studying the stress in the rotating thing ring
1646663324590.png


and find out the last equation that says
1646663393862.png

I would like to understand why?
Thank you!
 
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The radial and axial stresses acting on the surface of the ring are just the compressional stress from atmospheric pressure. Since the ring is very thin, these persist throughout the thickness of the ring.
 
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Chestermiller said:
The radial and axial stresses acting on the surface of the ring are just the compressional stress from atmospheric pressure. Since the ring is very thin, these persist throughout the thickness of the ring.
thanks a million!
 
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1. Why is the radial stress in a rotating thin ring null?

The radial stress in a rotating thin ring is null because the centrifugal force acting on the particles in the ring is balanced by the internal stress within the ring. This results in a state of equilibrium where the net force on the ring is zero, causing the radial stress to be null.

2. Why is the axial stress in a rotating thin ring null?

The axial stress in a rotating thin ring is null because the ring is rotating at a constant angular velocity. This means that the particles in the ring are not accelerating, resulting in no net force acting on the ring in the axial direction. Therefore, the axial stress is null.

3. How does the rotation of a thin ring affect its stress distribution?

The rotation of a thin ring causes the stress distribution to be non-uniform, with the highest stress occurring at the inner and outer edges of the ring. This is due to the centrifugal force acting on the particles, which creates a tensile stress at the outer edge and a compressive stress at the inner edge.

4. Can the radial and axial stress in a rotating thin ring ever be non-null?

Yes, the radial and axial stress in a rotating thin ring can be non-null if there are external forces acting on the ring, such as friction or external loads. In this case, the net force on the ring will not be zero, resulting in non-null radial and axial stresses.

5. How does the thickness of a rotating thin ring affect its stress distribution?

The thickness of a rotating thin ring does not significantly affect its stress distribution. As long as the ring is thin enough to be considered a membrane, the stress distribution will be the same regardless of its thickness. However, if the ring is thick enough to resist bending, the stress distribution will be different due to the presence of bending stresses.

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