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

Click For Summary

Discussion Overview

The discussion revolves around calculating the maximum rotational speed of a thin-walled hollow cylinder, specifically focusing on the conditions under which it may fail or "explode" due to centripetal forces. Participants explore the necessary parameters, such as tensile strength, radius, and density, while addressing the implications of rotation on the cylinder's structural integrity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) inquires about the parameters needed to calculate the maximum rotational speed of a hollow cylinder, suggesting that integration may not be necessary due to its thin-walled nature.
  • One participant questions the premise of the cylinder exploding, arguing that if it is empty, there may be no reason for it to fail, as centripetal force acts on the contents rather than the frame itself.
  • Another participant agrees with the OP's assertion that integration is not required and suggests analyzing a small section of the cylinder to derive the necessary forces and tensions involved in maintaining centripetal acceleration.
  • A later reply acknowledges confusion between centripetal and centrifugal forces, indicating a common misunderstanding in the discussion.
  • One participant proposes comparing the scenario with a cylinder under internal pressure, suggesting a relationship between internal pressure and the centrifugal forces experienced in a rotating frame.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which the hollow cylinder may fail, with some supporting the OP's approach while others challenge the assumptions regarding the cylinder's contents and structural behavior under rotation. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants have not fully clarified the assumptions regarding the cylinder's contents and the definitions of forces involved, leaving some aspects of the problem open to interpretation.

Bobcent
Messages
31
Reaction score
0
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!
 
Last edited:
Physics news on Phys.org
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!
 
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?
 
oops...i'm extremely sorry! always get confused with centripetal and centrifugal !
 
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.
 
Thanks for the help! :)
 

Similar threads

Undergrad Warm-up time for a hollow cylinder
  • · Replies 5 ·
Replies
5
Views
3K
High School Is it safe to fly in a spinning hollow asteroid?
  • · Replies 39 ·
2
Replies
39
Views
2K
Doublet flow in Fluid Dynamics between two spheres or cylinders
  • · Replies 0 ·
Replies
0
Views
2K
A block placed in a horizontal hollow cylinder
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Two ways to calculate the final speed of a rotating cylinder
  • · Replies 2 ·
Replies
2
Views
3K
How to determine how much torque a hollow cylinder can take?
  • · Replies 10 ·
Replies
10
Views
6K
Graduate Rotating Cylinder - Understanding Gas Pressure and Density
  • · Replies 1 ·
Replies
1
Views
6K
Undergrad How do I calculate the torque needed for a rotating cylinder?
  • · Replies 4 ·
Replies
4
Views
3K
Rotational Forces on a Hollow Cylinder
  • · Replies 4 ·
Replies
4
Views
3K
Graduate How is Maximum Sustained Speed Calculated for a Car Driving Up an Incline?
  • · Replies 6 ·
Replies
6
Views
2K