# Mass moment inertia of object displaced from axiz

• PTC
In summary, the conversation discusses the best approach for finding the mass moment of inertia for an object rotating around an axis. The two options are to develop an integral describing the mass distribution along the axis or use the parallel axis theorem. The speaker suggests using the first option as it would be easier to compute over the interval.

#### PTC

Hey y'all,

A plea for general advice here as I embark on a project. Say I have an object rotating around an axis but *displaced* some distance "r" from that axis. It's length, a dimension perpendicular to the axis, is "a." I'm interested in finding the mass moment of inertia for the object. As I see it, I have two choices: (1) develop an integral describing the mass distribution of the object around the axis and then use the fundamental theorem and the interval r to r+a or; (2) use the parallel axis theorem, that is, develop definitive integrals describing both the mass distribution of the object at r=0 and around the axis at r->r+a, summing the two. So real simply, fundamental theorem or parallel axis theorem?

Thanks!

PTC

I never really got my head round the parallel axis theorem, so I would use 1), which should be fairly easy, since the object is pointing straight away from the axis, it makes the integral fairly simple.

Thanks, Bruce! That's just about what I figured--it'd be much easier to compute over the interval. Thanks again!

PTC

## What is the mass moment of inertia of an object?

The mass moment of inertia of an object is a measure of its resistance to rotational motion. It is the sum of the products of each element of mass in an object multiplied by the square of its distance from a specified axis of rotation.

## How do you calculate the mass moment of inertia?

The mass moment of inertia can be calculated using the formula I = Σmr², where I is the mass moment of inertia, m is the mass of each element, and r is the distance of each element from the specified axis of rotation.

## What is the significance of the mass moment of inertia?

The mass moment of inertia is significant because it determines how much torque is needed to rotate an object around a specified axis of rotation. A larger mass moment of inertia means a greater amount of torque is required to achieve the same rotational motion.

## How does the displacement of an object affect its mass moment of inertia?

The mass moment of inertia is directly proportional to the square of the distance from the axis of rotation. This means that as an object is displaced further from the axis of rotation, its mass moment of inertia increases.

## Why is the mass moment of inertia important in engineering and physics?

The mass moment of inertia is important in engineering and physics because it is a crucial parameter in understanding and predicting rotational motion. It is used in the design of machines and structures, and in analyzing the behavior of objects in motion.