# Moment of inertia and contact force

• I
• GT1
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.

#### GT1

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?

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

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?

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.

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.

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GT1 and erobz

## 1. What is moment of inertia and why is it important?

Moment of inertia is a measure of an object's resistance to rotational motion. It is important because it helps us understand how an object will rotate when subjected to a force, and is essential in many engineering and physics applications.

## 2. How is moment of inertia calculated?

Moment of inertia is calculated by summing the products of each particle's mass and its squared distance from the axis of rotation. The formula is I = Σmr², where I is the moment of inertia, m is the mass of the particle, and r is the distance from the axis of rotation.

## 3. What factors affect the moment of inertia of an object?

The moment of inertia of an object depends on its mass distribution and the axis of rotation. Objects with more mass concentrated towards the axis of rotation will have a smaller moment of inertia than objects with mass distributed farther from the axis.

## 4. How does contact force affect an object's moment of inertia?

Contact force does not directly affect the moment of inertia of an object. However, the distribution of forces on an object can affect its rotational motion and therefore its moment of inertia. For example, pushing on a door at the hinges instead of the handle will result in a different moment of inertia for the door.

## 5. How is contact force related to torque and moment of inertia?

Contact force and torque are closely related to moment of inertia. Torque is the measure of a force's ability to cause rotational motion, and it is directly proportional to both the contact force and the distance from the axis of rotation. Therefore, the moment of inertia, which also depends on the distance from the axis of rotation, is indirectly affected by contact force through torque.