How do you calculate moment of inertia for circle?

In summary, the conversation discusses calculating the moment of inertia for a circle that is not at its center of gravity, specifically in two dimensional space. The parallel axis theorem may be used to avoid using an integral. The person has spent hours researching this topic but has not been able to find a solution. They have also looked at the Wikipedia page but are still unsure how to apply it. The concept of a reference point in the plane of the circle is also brought up.
  • #1
Josh The Cool
4
1
Hey, not sure if this is the right place to post this, but here it goes. how do you calculate the moment of inertia for a circle that is not at its center of gravity. I am trying to find the moment of inertia for a complex shape made of many circles, and this seems like a good place to start. Forgive me if the answer is simple, because I have spent hours googling this question and have come up empty handed. I would greatly appreciate any help!
 
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  • #3
This is in two dimensional space. So I think the z axis if I understand correctly.
Edit:
I also looked at that wiki page, but couldn't apply it in any useful way.
 
  • #4
What is unclear about the Wikipedia page?
 
  • #5
Are you thinking of a reference point in the plane of the circle but not at the center of the circle?

A circle is a purely geometric figure, and as such, has no cg. It does have centroid; is that what you have in mind?
 

1. What is the formula for calculating moment of inertia for a circle?

The formula for calculating moment of inertia for a circle is I = 1/2 * m * r^2, where I is the moment of inertia, m is the mass of the object, and r is the radius of the circle.

2. How does the shape of the circle affect its moment of inertia?

The shape of the circle does not affect its moment of inertia, as it is a constant value for any circle regardless of its size or shape.

3. Can moment of inertia be negative for a circle?

No, moment of inertia cannot be negative for a circle as it is a measure of an object's resistance to change in rotational motion. Any negative value would not make sense in this context.

4. What is the unit of measurement for moment of inertia?

The unit of measurement for moment of inertia depends on the units used for mass and radius in the formula. Generally, it is measured in kg*m^2 or g*cm^2.

5. How is the moment of inertia of a circle related to its angular acceleration?

The moment of inertia of a circle is directly proportional to its angular acceleration. This means that a circle with a larger moment of inertia will have a slower angular acceleration compared to a circle with a smaller moment of inertia, for the same applied torque.

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