Moment of inertia and contact force

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SUMMARY

The moment of inertia of a system involving rotating cylinders or a belt and pulley system is independent of the contact force (F1) and the tension in the belt. The moment of inertia is defined by the equation $$I=\int \rho r^2 \ dV$$, which incorporates mass and the distribution of that mass relative to the axis of rotation, not external forces. While increased contact force can lead to greater friction and rolling resistance, it does not alter the moment of inertia itself. Effective power transfer can be compromised by excessive forces due to increased friction and heat, but the fundamental inertia remains constant.

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  • Understanding of moment of inertia and its mathematical definition
  • Basic knowledge of rotational dynamics
  • Familiarity with friction and its effects on mechanical systems
  • Concept of mass distribution in relation to rotational axes
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  • Explore the relationship between contact forces and energy loss in rotating systems
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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?
 
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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
 
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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?
 
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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.
 
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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
 
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