How to calculate compression of a spring

[Gazi]

centrifugal force apply force to spring while it spinning, how to calculate it's compression. there is no any attached mass on spring. just centrifugal force depends on RPM. weight of spring is important, centrifugal force is changing by radius, so it's not uniform.

 

[Drakkith]

If the change in radius is small compared to the overall radius, then I'd assume a constant r and model the spring as having a small mass attached to the end of it. Then you can find the force on that mass and use hooke's law to find how far the spring is compressed.

 

[muscaria]

Alternatively, if you considered the mass of the spring was uniformly distributed from the origin to the radius, then you could use the moment of inertia of a rod about its end i.e $I=\frac{1}{3}mr^2$ with associated angular momentum $L=I\omega$. In doing this you're basically attaching all the mass contributing to angular momentum to a point along the spring which is $1/\sqrt{3}=0.577$ along the spring, i.e. between a half and 2/3 of $r$. There is then an associated centripetal force from which you can get the extension as Drakkith suggested.

 

[Gazi]

inertia moment of long uniform rod through end is I=1/3ML² what if rod has hollow. what is inertia moment?