Angular speed that breaks a spinning body apart with inertial stress

In summary, the conversation discusses the calculation of tangential and radial stresses on a spinning hollow cylindrical body, and how to determine if the body will break due to these stresses. Different sources offer different formulas and theories, such as using principal stresses and a failure theory. It is also mentioned that the material properties of the body and its state (e.g. annealed, hardened) need to be considered in determining if it will break. Overall, the question of determining whether a metal body will break is complex and cannot be easily answered without more specific information.
  • #1
olgerm
Gold Member
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How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)?
I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) , https://www.engineersedge.com/mechanics_machines/solid_disk_flywheel_design_14642.htm (eq. 4) ) that offer different formulas to calculate tangential and radial stresses. One of them claims that maximum radial stress is at ##r=\sqrt{r_1*r_2}## and other one that it occurs at ## r=0##. Which one of these is correct?
Is it that the body breaks if
##\sigma_{tangential}>\sigma_{ultimate\ stress}\ or\ \sigma_{radial}>\sigma_{ultimate\ stress}##
or if
##(\sigma_{tangential}^2+\sigma_{radial}^2)>\sigma_{ultimate\ stress}^2##
 
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  • #2
More generally how determine if a body breaks if I know stress tensor appllyied on that body and mechanical propetis of that body?
 
  • #4
I heard that it has something to do with principal stresses. Can someone explain that to me with more details how to determine whether body breaks based on principal stresses applied on the body?
 
  • #5
olgerm said:
More generally how determine if a body breaks if I know stress tensor appllyied on that body and mechanical propetis of that body?
What about simple case when it pushed from 2 sides so that the stress tensor is:
##\begin{bmatrix}
\sigma_{xx}&0 &0 \\
0&\sigma_{yy}&0\\
0&0&0
\end{bmatrix}##
How to know if a body breaks under this stress?
 
  • #6
You will need to know something about the material properties (is it brittle or will it deform plastically?) and you will need a failure theory. The inputs to most failure theories are the principal stresses, so you are part way there.
 
  • #7
Dr.D said:
you will need a failure theory.
Which criterion should In use to determine whether a metal body breaks into pieces or not?

Is one of these good approximation?
olgerm said:
body breaks if
##\sigma_{tangential}>\sigma_{ultimate\ stress}\ or\ \sigma_{radial}>\sigma_{ultimate\ stress}##
or if
##(\sigma_{tangential}^2+\sigma_{radial}^2)>\sigma_{ultimate\ stress}^2##
 
  • #8
The question is too broad. You have to specify what the metal is and what its state is (annealed, hardened, drawn, etc.). This is not a simple question, and not the sort of thing that can be adequately answered on PF.
 

1. What is angular speed?

Angular speed is a measure of how quickly an object rotates around a fixed axis. It is usually measured in radians per second or degrees per second.

2. How does angular speed affect a spinning body?

Angular speed can cause a spinning body to experience inertial stress, which is a force that acts to pull the object apart. This stress can increase as the angular speed increases.

3. What is the relationship between angular speed and inertial stress?

The higher the angular speed of a spinning body, the greater the inertial stress it will experience. This is because the faster the body rotates, the more force is exerted on it, causing it to potentially break apart.

4. How can angular speed be calculated?

Angular speed can be calculated by dividing the angle through which an object rotates by the time it takes to complete the rotation. This can be represented by the equation ω = Δθ/Δt, where ω is the angular speed, Δθ is the change in angle, and Δt is the change in time.

5. What are some factors that can influence the angular speed that breaks a spinning body apart?

The angular speed that causes a spinning body to break apart can be influenced by factors such as the mass, shape, and material of the object, as well as the speed of rotation and any external forces acting on the body.

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