The Moments of Inertia: Difference between revisions
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This page discusses the | This page discusses the idea of inertia as it relates to angular motion | ||
Written by Jack Corelli | |||
(claimed by sans47) | |||
==The Main Idea== | |||
Inertia of a solid mass is a simple concept. As described by Newton's laws, objects tend to keep doing what they are currently doing, ie. they resist change. Inertia is a 'measure' of this. A larger, more massive object is said to have more inertia, as it would resist change more than a smaller, less massive object. This is a simple concept to apply in 1d motion. For a constant force, increasing mass lowers acceleration, and vice versa. However, the same equation can still apply in 2d motion, it is however split into its component x and y in order to simplify calculations. | |||
In 2d rotational motion, a new description is needed to describe an objects inertia, and this is aptly named a 'moment of inertia'. Simply put, moments of inertia refer to an objects resistance to change in 2d rotational motion. In other words, when talking about moving in a straight line, the governing equation F = m*A is adequate to describe the relationship between mass and acceleration. In rotational motion, the mass of an object is not adequate in describing how the shape, distribution of mass, and total mass impact the acceleration of an object. Thus, a moment of inertia is needed to fully describe this relationship. In rotational motion, the moment of inertia of an object relates three things: | |||
1. The mass of the object | |||
2. The distance between the center of mass and the axis of rotation | |||
3. The shape of the object being rotated | |||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Revision as of 17:21, 30 November 2015
This page discusses the idea of inertia as it relates to angular motion Written by Jack Corelli (claimed by sans47)
The Main Idea
Inertia of a solid mass is a simple concept. As described by Newton's laws, objects tend to keep doing what they are currently doing, ie. they resist change. Inertia is a 'measure' of this. A larger, more massive object is said to have more inertia, as it would resist change more than a smaller, less massive object. This is a simple concept to apply in 1d motion. For a constant force, increasing mass lowers acceleration, and vice versa. However, the same equation can still apply in 2d motion, it is however split into its component x and y in order to simplify calculations.
In 2d rotational motion, a new description is needed to describe an objects inertia, and this is aptly named a 'moment of inertia'. Simply put, moments of inertia refer to an objects resistance to change in 2d rotational motion. In other words, when talking about moving in a straight line, the governing equation F = m*A is adequate to describe the relationship between mass and acceleration. In rotational motion, the mass of an object is not adequate in describing how the shape, distribution of mass, and total mass impact the acceleration of an object. Thus, a moment of inertia is needed to fully describe this relationship. In rotational motion, the moment of inertia of an object relates three things: 1. The mass of the object 2. The distance between the center of mass and the axis of rotation 3. The shape of the object being rotated
A Mathematical Model
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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