- #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##

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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