How do I calculate the maximum rotational speed of a hollow cylinder?

[Bobcent]

Hello!

How do I calculate the maximum possible rotational speed of a thin walled hollow cylinder? In other words, at what rotational speed will it explode due to centripetal force?

This picture shows the plane of rotation:

http://www.ithaca.edu/faculty/mcsullivan/PH117/CTs/CT-ParallelAxisThereom-IMAGES/HollowCylinder.gif

All I need to know is:

Tensile strength of the material of the cylinder

Radius

Density of the material of the cylinder

Nothing more, right?

Because the cylinder is hollow and thin walled it shouldn't be necessary to integrate, right?

Thanks in advance!

 

[deep838]

i believe there must be some substance inside the cylinder that will cause it to explode! otherwise, if its empty, why will it explode? doesn't the centripetal force act only on the things 'inside' a rotating frame? i don't think it acts on the frame itself!

 

[jbriggs444]

Explode. Tear itself apart. Be unable to provide the centripetal force required to maintain the centripetal acceleration associated with the rotation. If you rotate the cylinder fast enough, it will fail to hold together.

OP is correct that you don't have to integrate to solve this. Consider a small section of the cylinder. The whole cylinder spans 2 pi radians. You just want to look at the portion that spans a small angle.

Draw a free body diagram for this section.
What is the mass of the section as a function of the angle that it spans and the mass of the whole cylinder?
What is the centripetal acceleration of this section?
What force is required to sustain the acceleration?
The cylinder material is under tension. Can you express the net force on the small section in terms of the angle that it spans and the tension in the cylinder walls?

 

[deep838]

oops...i'm extremely sorry! always get confused with centripetal and centrifugal !

 

[AlephZero]

You might like the compare this with the same question about a cylinder with internal pressure. The two are closely related, if you compare the pressure with the "centrifugal force" acting on the cylinder when you model it in a rotating coordinate system.

 

[Bobcent]

Thanks for the help! :)