246
ON
THE
INERTIA
OF ENERGY
one
realizes that the electrostatically
charged
body
has
an
inertial
mass
that
exceeds
that of the
uncharged
body by
the electrostatic
energy
divided
by
the
square
of
the velocity
of light.
The law
of
the inertia
of
energy
is thus
confirmed
by
our
result in the special
case
considered.
§3. Remarks
concerning the
dynamics
of
the rigid
body
From
the
foregoing
it
might
seem
that
we are no
longer
far
from the
goal
of constructing
a dynamics
of
the parallel translation
of
the rigid
body
that
would
conform to
the
principle of
relativity.
However,
one
must remember
that
the
investigation
carried
out
in
§1
yielded
the
energy
of
a
rigid
body
subjected to
forces
only
for the
case
that these forces
are
constant
in time.
If
at
the
time
t1
the
forces
X' depend
on
the time, then
the
work
E,
and
thus also the
energy
of the rigid
body, proves
to
be dependent not only
on
those forces that
occur
at
one
particular
time.
To
illustrate the
difficulty
involved
as
drastically
as
possible, let
us
imagine
the following simple
special
case. We
consider
a
rigid
rod
AB
which
shall
be at
rest
relative
to
a
coordinate
system
(£,n,(),
with
the
rod
axis
resting
in the
(-axis.
At
a
certain time
r0
let
equal
but
opposite
forces
P
act
on
the rod ends
for
a
very
short time, while
at
all other times the
rod
is
not subjected to
forces. It is
obvious
that the
above
action
on
the
rod at
time
t0
does not
produce
any
motion
of the rod.
We now
observe
the
very
A
B
v
same
process
from
a
coordinate
system
whose
axes are
parallel
to
those
of
the
system
used
earlier, relative
to
which
the
rod
moves
in
the direction
A-B
with
velocity
v.
However,
viewed from
this coordinate
system,
the
impulses
in
A
and
B
do
not act
simultaneously;
rather, the
impulse
in
B
is
delayed
by
lß(v/V2)
time units with
regard
to
the
impulse
in
A,
where
l
denotes the
length
of
the
rod
(measured
at
rest).
Thus
we
arrived
at
the
following
odd-looking
result.
On
the
moving
rod
AB, an
impulse
acts
first in
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