What is the Moment of Inertia for a Hollow Torus?

Click For Summary

Discussion Overview

The discussion centers around the calculation of the moment of inertia (MOI) for a hollow torus, specifically in the context of its rotation about a horizontal axis. Participants explore different formulas and approaches to derive the MOI for this shape, considering its mass and dimensions.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant requests the formula for the moment of inertia for a hollow torus with specific dimensions and mass.
  • Another participant confirms that the discussion pertains to the moment of inertia for a torus.
  • A question is raised about whether the provided formula applies to rotation around a horizontal axis, as existing references show configurations for vertical axes.
  • It is noted that there are three principal axes for a torus, with two having the same moment of inertia, and that the linked page provides formulas applicable for deriving expressions for any axis.
  • A participant suggests using the moment of inertia for a solid torus and subtracting the solid torus of the inner radius to find the moment of inertia for the hollow torus, emphasizing that mass considerations must be taken into account.
  • Another participant verifies the moment of inertia for a solid torus and questions whether the same assumption can be made for a hollow torus regarding the equivalence of horizontal and diameter axis MOI.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the application of formulas for different axes of rotation and whether the same assumptions hold for hollow versus solid tori. No consensus is reached on the equivalence of the moment of inertia for the hollow torus across different axes.

Contextual Notes

Participants express uncertainty about the applicability of certain formulas to different axes of rotation and the implications of mass differences between solid and hollow tori. There are unresolved aspects regarding the derivation of the moment of inertia for the hollow torus.

raj26
Messages
18
Reaction score
0
I would like to know the formula for Moment of inertia for horizontal rotation of circular tube(i.e wheel) of mass 65kg, wheel dia=2m, tube dia=0.1m.
 
Physics news on Phys.org
But is the formula you have told applies for rotation around a horizontal axis? The figure shown in wiki is for vertical configuration.
 
There are 3 principal axis. 2 of them have the same moment of inertia about them. The page I linked to gives you two formulae. You can use these to derive expression for ANY axis.
 
Thanks for your answers...Actually i needed MOI for a hollow torus ...I got the two MOI expressions.

O
 
Last edited:
For hollow torus, take MOI for solid torus with outer radius, and subtract solid torus of inner radius. MOI is additive, so this should give you correct answer. Just keep in mind that the mass would be greater if the torus was solid. You need to account for that.
 
One last Q: I verified your answer for the case of solid torus on the net and found that horizontal axis MOI and the diameter axis MOI are the same. Can i assume the same for a hollow torus. (Again i have MOI for it for two axes and i need for the horizontal one!)
 

Similar threads

Undergrad How to find moment of inertia of an insect?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Is it possible to create linear acceleration using nothing but different moments of inertia beteen a wheel and axle?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Resolve moment of inertia at an angle
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Energy Transfer Between Inertia Wheels
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How find moment of inertia for car in turn?
  • · Replies 49 ·
2
Replies
49
Views
6K
High School The physics of flywheel launchers (like tennis ball shooters)
  • · Replies 60 ·
3
Replies
60
Views
7K
Undergrad How to quantify gyroscopic precession torque?
  • · Replies 49 ·
2
Replies
49
Views
5K
Undergrad Moment of inertia of human body with limbs at an angle
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad How Is Power Calculated in a Rotating System with Variable Speed?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Moment of inertia where mass and torque are at a different positions
  • · Replies 69 ·
3
Replies
69
Views
6K