What is Inertia

[John Hartman]

Richard Brekne wrote:

 > I think it would be for the best, and I am sure you will agree, if we
 > get any and all possible misconceptions or easily misconstrued
 > formulations cleared up so we can all be on the same page when we are
 > refering to these terms.


Richard,

I am not sure I can clear this up but I will give it  a try. The Moment
of inertia is a quantity we give a body to describe its mass if it is
rotating around a point. Moment of inertia takes the place of mass in
figuring motions of rotating bodies. In studying the motions of bodies
moving in a straight line (translation) we use the mass of the body as 
its inertia (inertia is a property of mass) but in studying the motions 
of rotating bodies the MOI is used instead.

There are other terms used for rotating bodies that are used instead of
the more familiar terms used in linear physics.

Angular velocity instead of velocity. w instead of v.
Angular acceleration instead of regular acceleration. w^2 instead of a.
Torque instead of Force. I(inercia)*w^2 instead of m*a.
Angular momentum instead of momentum. I*w instead of m*v.

The most simple case of MOI is that of a small object tied to a string
rotating around a point. In this case the MOI can be found by weighing
the object and measuring the radius of the circle it travels in. I=MR^2.
The MOI of complex objects can be found by dividing into many small 
points of mass and measuring their distance from the point of rotation. 
Use the formula M*R^2 on all of them and add them all together.

The MOI of some basic shapes can be found with calculus and are commonly
known. A bar rotating around its center is 1/12ML^2 for example. Many
others are known as well.

Once you know the MOI you can use it to find how much acceleration a
body would gain if acted on by a known Torque.

John Hartman RPT

John Hartman Pianos
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