Moment of inertia and contact force

In summary: In-summary-the-moment-of-inertia-of-a-system-does-not-depend-on-the-force-contact-force-ofIn summary, the moment of inertia of a system does not depend on the force contact force of the system.
  • #1
GT1
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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?
 
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Homework?
 
  • #3
erobz said:
Homework?
No. Real life question..
 
  • #4
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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  • #5
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?
 
  • #6
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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  • #7
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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  • #8
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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FAQ: Moment of inertia and contact force

What is the moment of inertia?

The moment of inertia, also known as the rotational inertia, is a measure of an object's resistance to changes in its rotation about an axis. It depends on the mass of the object and how that mass is distributed relative to the axis of rotation. Mathematically, it is represented as I = Σmr², where m is the mass of each particle and r is the distance of each particle from the axis of rotation.

How is the moment of inertia different from mass?

While mass is a measure of the amount of matter in an object and is a scalar quantity, the moment of inertia is a measure of how that mass is distributed with respect to an axis and is a tensor quantity. Mass affects linear motion, whereas the moment of inertia affects rotational motion. An object with a larger moment of inertia will be harder to rotate.

What factors affect the moment of inertia of an object?

The moment of inertia of an object is affected by its mass and the distribution of that mass relative to the axis of rotation. For example, a solid disk and a ring of the same mass and radius will have different moments of inertia because their mass distributions are different. The shape and the axis about which the object rotates are crucial factors.

What is a contact force?

A contact force is a force that acts at the point of contact between two objects. Examples of contact forces include friction, normal force, tension, and applied forces. These forces arise from the physical interaction between objects and can cause changes in motion according to Newton's laws of motion.

How are moment of inertia and contact force related in rotational motion?

In rotational motion, the moment of inertia and contact forces are related through the dynamics of the system. For example, when a rolling object (like a wheel) makes contact with a surface, the frictional force at the contact point can affect its rotational motion. The moment of inertia determines how the object responds to these forces, influencing its angular acceleration and overall rotational behavior.

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