Last moment of inertia problem I have

In summary, the problem involves finding the moment of inertia of a system of four small spheres arranged in a square and connected by light rods. The moment of inertia is to be calculated about an axis passing through the center of the square and perpendicular to its plane. The relevant equation for this problem is I = mr^2. The solution involves finding the distances of the particles from the axis of rotation, which can be done using components and trigonometry. The detailed calculations are not provided in the conversation.
  • #1
elsternj
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0

Homework Statement


Four small spheres, each of which you can regard as a point of mass 0.200kg , are arranged in a square 0.400m on a side and connected by light rods .

Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure).

YF-09-29.jpg



Homework Equations


I = mr2


The Attempt at a Solution



Okay now where I am having trouble with this one is finding the distances of these particles from the axis of rotation. When thinking on it, It seemed that I could use components to find a vector that reaches out to the particles. (the y and x components would both be .2m and the angle at 45degrees). But in doing this, my answer wasn't right. I don't know if I am missing something mathematically here but how does one go about finding that distance?
 
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  • #2
Show the calculations in detail.

ehild
 

Related to Last moment of inertia problem I have

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is often referred to as "rotational inertia" or "angular mass".

2. How is moment of inertia calculated?

The moment of inertia of a point mass is equal to the mass multiplied by the square of the distance from the axis of rotation. For a continuous object, it is calculated by integrating the individual moments of inertia of all its infinitesimal parts.

3. What is the significance of moment of inertia?

Moment of inertia is important in understanding the behavior of rotating objects, as it affects their acceleration, speed, and stability. It is also used in designing machines and structures that involve rotational motion.

4. What is the difference between moment of inertia and mass?

Moment of inertia is a property of an object related to its distribution of mass, while mass is a measure of the amount of matter an object contains. In other words, mass determines an object's inertia in linear motion, while moment of inertia determines its inertia in rotational motion.

5. How is moment of inertia affected by the shape of an object?

The moment of inertia of an object depends on both its mass and its distribution of mass. Objects with more mass located farther away from the axis of rotation will have a larger moment of inertia, while objects with more mass located closer to the axis will have a smaller moment of inertia.

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