What is Inertia

[Richard Brekne]

Hi Jim and Don.

I cant help but thinking there is some significant difference between
the definitions of inertia each of you give below. Don seems to insist
that inertia is totally independant of velocity or accelleration. That
inertia is the same for an object moving at 10 m/sec as it is for one at
rest, or for that matter moveing at 10000 m/sec. Ditto for the
measureable quantity of moment of intertia. But Jim seems to be saying
that both inertia as a property, and moment of inertia as a measureble
quantity is acceleration dependant... ie that the faster a thing is
changing speed the more inertia it has.  In particular Jim says

" The velocity, or speed, of a mass revolving about a central point is
proportional to the radius of the orbit of that mass.  Therefore, the
moment of inertia is proportional to the square of the radius, or the
square of the acceleration or decelaration."

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. 

Thanks

RicB


"Don A. Gilmore" wrote:
> 
> Gentlemen:
> 
> I think I can straighten out the concept of inertia with a single statement:
> 
> ***An object exhibits the effects of inertia even if it is standing
> still.***
> 
> Inertia is just the stubborn tendency of matter to resist change (kind of
> like me).  Matter resists a change in its velocity (acceleration).  That
> change can be from sitting still to 10 m/s, or it could be changing it from
> 100 m/s to 110 m/s.  It resists in the form of force (or torque, for a
> rotating object).
> 
> F = m * a, for linear motion in a straight line
> T = J * [alpha], for rotary motion about an axis
> 
> Where F is force (newtons, or lbs), m is mass (kg, or slugs), a is
> acceleration (m/s^2, or ft/s^2), T is torque (N-m, or lb-ft), J is moment of
> inertia (kg-m^2, or slug-ft^2) and [alpha] is angular acceleration in
> radians per second squared.  Note that velocity is not involved.  It takes
> the same amount of force to accelerate an object from rest as it does if
> it's travelling at 1000 mph.
> 
-------------------------
Jim Ellis wrote

Inertia is a minifestation, a property, an effect, of acceleration and
deceleration.  It's proportional to the square of the change in speed,
or
velocity.  Acceleration and deceleration are changes in velocity.  The
velocity, or speed, of a mass revolving about a central point is
proportional to the radius of the orbit of that mass.  Therefore, the
moment of inertia is proportional to the square of the radius, or the
square of the acceleration or decelaration.  If you are slinging a rock
in
a sling at the rate of two RPS, its force on the sling will be four
times
what it would be at one RPS.  In the case of the rock in the sling, we
are
dealing with centripetal acceleration.  These are just different
manifestations of the same thing.  Inertia is simply the resistance a
mass
has to being accelerated or decelarated, or forced to change direction.
You will find this discussed in a variety of textbooks.