# Find the moment of inertia of a washer

• Pablo
In summary, the moment of inertia of a washer with a hole of radius r/2 can be found using the integral of x^2 dm, where γ is equal to the linear density of the washer and L is the length of the washer. However, if the washer is a three-dimensional object, the expression for dm may need to be adjusted to account for its volume. Additionally, it would be helpful to have a diagram or more information about the dimensions of the washer in order to accurately calculate the moment of inertia.
Pablo

## Homework Statement

Find moment of inertia of a washer with a hole of radius r/2.

## Homework Equations

Moment of inertia = integral of x^2 dm
γ = m / L

## The Attempt at a Solution

I think I can find the moment of inertia of the washer using integral of x^2 dm. So, I know my γ = m / L = m / (R/2) = 2m / R

I = (2m / R) * [((R/2)^3 / 3) - 0] = (m * R^2) / 12

However, that is not correct. Where am I going wrong?

Is there a diagram that shows the washer's dimensions? Is it a thick washer or a thin washer?

Also, you can find a LaTeX tutorial under INFO at the top of the page. Click on Help/How-To. That will help you post with math equations that are much easier to read and respond to.

Pablo said:
γ = m / L
What are γ and L? This looks like an expression for linear density, but a washer has area.

This looks like a three-dimensional problem. What is your expression for dm?

Dr Dr news said:
This looks like a three-dimensional problem. What is your expression for dm?
No, I think it is just a lamina. No thickness is given.

## 1. What is the definition of moment of inertia?

The moment of inertia is a measure of how much an object resists rotational motion. It is the sum of the products of each particle's mass and its squared distance from the axis of rotation.

## 2. How is moment of inertia calculated?

The moment of inertia of a washer can be calculated by using the formula I = (1/2)MR^2, where M is the mass of the washer and R is the radius of the washer.

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

Moment of inertia is a measure of an object's resistance to rotational motion, while mass is a measure of an object's resistance to linear motion. In other words, moment of inertia describes how an object's mass is distributed around its axis of rotation.

## 4. How does the shape of an object affect its moment of inertia?

The shape of an object can greatly affect its moment of inertia. Objects with a larger radius, such as a washer, have a greater moment of inertia compared to objects with a smaller radius. The distribution of mass also plays a role in determining moment of inertia.

## 5. Why is moment of inertia important in science and engineering?

Moment of inertia is important in understanding the rotational motion of objects, such as in the design of machines and structures. It also plays a crucial role in the conservation of angular momentum, which is a fundamental concept in physics.

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