Re: Apparent weight

[Leigh Palmer <palmer@sfu.ca>]

> The rotating earth is a non-inertial frame of reference. What I have
> been referring to as weight measured by the bathroom scale is the normal
> force exerted by the scale. In an inertial frame of reference, N=mg
> numerically.
> F(net) = ma (in general)
> or N-mg=ma
> If a=0 as in static equilibrium, then
> N-mg=0
> and N=mg
> However, the rotating earth is a non-inertial frame of reference and we
> must write
> N-mg=-mv^2/r
> or N=mg-mv^2/r .
> Since the last term is small, I said that N was nearly equal to mg.
>
> Roger Pruitt

Weight is something that can be measured. We all know how to measure
it; we use a scale (or "forcemeter" as some would have it). Weight
is not an intrinsic property of an object; it is an attribute of an
object relative to a particular frame of reference. For example, the
weight of an object on the surface of Earth varies with latitude, and
it is different on the surface of the Moon, and in the space shuttle.

As I've pointed out, and cited in all those books, most explicitly in
David Hestenes's text, the centrifugal acceleration *is* part of the
quantity which is conventionally called "g". W = mg . You are making
the error of treating centrifugal force as a separate force; it is
not a separate force. I'm unclear as to what "N" might be; you have
not explained that at all, though you may believe you have done so.

The surface of the nonrotating Earth is also a non-inertial frame of
reference. You have been operating under the illusion that it is an
inertial frame. The law of inertia clearly does not hold on Earth's
surface, but you have accounted for this nonconformity by inventing
a fictitious force (which you call a "noncontact force" though it is
more commonly referred to as "action at a distance") which you call
"gravity". Einstein follows the line of reasoning that starts with
the observation that there is locally no way to tell the difference
between a gravitational field and an accelerated frame. The result,
general relativity, was capable of predicting results unknown at the
time the theory was formulated. Thus one may be persuaded that the
principle upon which it was based is a valid world view.

Leigh