# Calculating the moment of inertia for this configuration

• Demon117
In summary, the conversation discusses finding the rotational kinetic energy of a system with a spring rotating at angular speed ω and three beads held by two massless rods of equal length L. The suggested solution involves calculating the moment of inertia about the z-axis, which may depend on the angle α.
Demon117

## Homework Statement

I need to find the rotational kinetic energy of this system in the figure I have provided. Here the spring is rotating with the system at angular speed $\omega$. The two beads on the wire move vertically, and the third bead is held by two massless rods of equal length L.

## The Attempt at a Solution

Would the moment of inertia for the the whole thing just be

$I_{1,3}=2mL^{2}$

$I_{2,3}=2mL^{2}$

$I_{total}=4mL^{2}$

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Demon117 said:

## Homework Statement

I need to find the rotational kinetic energy of this system in the figure I have provided. Here the spring is rotating with the system at angular speed $\omega$. The two beads on the wire move vertically, and the third bead is held by two massless rods of equal length L.

## The Attempt at a Solution

Would the moment of inertia for the the whole thing just be

$I_{1,3}=2mL^{2}$

$I_{2,3}=2mL^{2}$

$I_{total}=4mL^{2}$

It looks as though the system is constrained to rotate about the z-axis.

You need to find the moment of inertia about the z-axis.

Will it depend on the angle $\alpha$?

Demon117 said:
Will it depend on the angle $\alpha$?

Yes it will depend on α .

I would like to clarify that the moment of inertia is a measure of an object's resistance to rotational motion and is dependent on the distribution of mass and the axis of rotation. In this case, the moment of inertia for the entire system would not simply be the sum of the moment of inertia for each individual component.

To accurately calculate the moment of inertia for this configuration, we would need to consider the contributions from each component, such as the two beads on the wire and the third bead held by the rods, as well as the spring and its rotational motion. This would involve using the parallel axis theorem and possibly integrating over the entire system to account for the distribution of mass.

Additionally, to calculate the rotational kinetic energy of the system, we would need to know the moment of inertia and the angular velocity, not just the moment of inertia. I would suggest consulting with your textbook or a reliable source for the appropriate equations and steps to calculate the moment of inertia and rotational kinetic energy for this specific system.

## What is moment of inertia and why is it important in science?

The moment of inertia is a measure of an object's resistance to changes in its rotation. It is important in science because it helps us understand how objects move and behave when they are rotating.

## How is moment of inertia calculated?

The moment of inertia for a given object can be calculated by summing the products of each particle's mass and its squared distance from the axis of rotation. This can be expressed mathematically as 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.

## What factors affect moment of inertia?

The moment of inertia of an object can be affected by its mass, shape, and distribution of mass. Objects with larger mass and more spread out mass distribution will have a higher moment of inertia, while objects with smaller mass and more concentrated mass distribution will have a lower moment of inertia.

## How is moment of inertia used in real-world applications?

Moment of inertia is used in a variety of real-world applications, such as designing structures that can withstand rotational forces, calculating the stability of rotating objects like satellites, and predicting the behavior of objects in motion, such as a spinning top or a swinging pendulum.

## Can the moment of inertia be negative?

No, the moment of inertia cannot be negative. It is a physical property of an object and therefore must have a positive value. However, the direction of rotation can be taken into account when calculating moment of inertia, resulting in a negative sign in the equation. This indicates the direction of rotation, not the actual value of the moment of inertia.

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