Moment of inertia and contact force

Click For Summary

Discussion Overview

The discussion revolves around the relationship between moment of inertia and contact forces in rotating systems, specifically focusing on two scenarios: rotating cylinders in contact and a belt and pulley system. Participants explore whether the moment of inertia is influenced by external forces such as contact force and belt tension.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions if the moment of inertia of a system depends on the contact force F1 applied between two rotating cylinders.
  • Another participant asserts that the moment of inertia is defined as $$I=\int \rho r^2 \ dV$$, suggesting that forces do not influence this definition.
  • A participant challenges the assertion that the effective mass felt by the cylinders is the same in different scenarios, asking for clarification on this point.
  • It is proposed that greater contact force may lead to increased friction and rolling resistance, but this is stated to not affect the moment of inertia itself.
  • A summary reiterates that both contact force and belt tension primarily affect load on bearings and do not alter the moment of inertia, which depends solely on mass distribution relative to the axis of rotation.

Areas of Agreement / Disagreement

Participants express differing views on the influence of contact forces and tension on moment of inertia, with some asserting that these forces do not affect inertia while others raise questions about the implications of increased friction and resistance.

Contextual Notes

Some participants highlight that while contact forces and tension may not change the moment of inertia, they can impact friction and heat, which are relevant in practical applications.

GT1
Messages
129
Reaction score
0
TL;DR
Moment of inertia and contact force
Two rotating cylinders are held in contact by a force F1. The force is applied through the center of one of the cylinders. One cylinder is the driving cylinder and the other is the driven cylinder .

Does the moment of inertia of the system depends on the force contact force F1? Why?


And another similar question –

In a belt and pulley system – does the moment of inertia of the system affected by the tension of the belt? Why?
 
Physics news on Phys.org
Homework?
 
erobz said:
Homework?
No. Real life question..
 
No to both. The moment of inertia is defined as $$I=\int \rho r^2 \ dV$$ so forces do not enter in to the expression
 
  • Like
Likes   Reactions: erobz
Dale said:
No to both. The moment of inertia is defined as $$I=\int \rho r^2 \ dV$$ so forces do not enter in to the expression
If in one case the mass of the cylinder is 100kg and in the second case the mass of the cylinder is 10kg and I'm pressing it at force of 90kg, in both cases it feels like the cylinder mass is 100kg.

What is the intuitive reason why in one of the cases it will be more difficult to accelerate the cylinder?
 
GT1 said:
in both cases it feels like the cylinder mass is 100kg
That is not true. Can you explain why you think that?
 
  • Like
Likes   Reactions: GT1
GT1 said:
What is the intuitive reason why in one of the cases it will be more difficult to accelerate the cylinder?
In a real world setup a greater contact force can cause more friction at the axles and greater rolling resistance due to more deformation. But that has nothing to do with the moment of inertia.
 
  • Like
Likes   Reactions: GT1 and erobz
GT1 said:
TL;DR Summary: Moment of inertia and contact force

Two rotating cylinders are held in contact by a force F1. The force is applied through the center of one of the cylinders. One cylinder is the driving cylinder and the other is the driven cylinder .

Does the moment of inertia of the system depends on the force contact force F1? Why?


And another similar question –

In a belt and pulley system – does the moment of inertia of the system affected by the tension of the belt? Why?
Both, F1 (the pressing force between rollers) and the tension of the belt, only put load on the bearings supporting the axles.
If excessive, that increases friction and heat, reducing effective transferred power.

The moment of inertia of the systems does not depend on those forces or friction.
It depends only on masses and their average distances to the axes of rotation of rollers or pulleys.
The inertia is only important for changes of rotational velocity, during the start up process.

For the pulleys for belts, you can reduce their moment of inertia by reducing diameter, but then, the belt must wrap and bend around a reduced radius, which increases internal friction and heat in the belt: again, wasting energy for as long as the mechanism is working.

Research frictional gears.

p1.jpg

https://www.calameo.com/read/006229255137154b6ea2e
 
Last edited by a moderator:
  • Like
Likes   Reactions: GT1 and erobz

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 49 ·
2
Replies
49
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 69 ·
3
Replies
69
Views
6K
  • · Replies 30 ·
2
Replies
30
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K