DOC.
1
MECHANICS LECTURE NOTES
5
(b)
But
this law does not
hold for
an arbitrary
state
of motion of the
c.s.
But
it holds to
a
certain
degree
of
approximation
for
systems
at
rest relative to
the
earth,
and
to
an even
closer
approximation
for
a
system
whose
origin is at rest
relative
to
the
center
of
gravity
of the
solar
system,
and
whose
axes are
directed
permanently
toward
3
fixed stars.
2. If other
bodies
act
upon
a
material
point,
the acceleration
vector
dhc
cPy
d2z
dt2' dt2'
dt2
is
generally
different
from
zero. The
cause
of
the
acceleration of
a
m.p.
is
called
a
force.
We
have
a
certain direct
representation
of
force,
and
this is
the
feeling
of exertion
or
pressure
that
we
experience when,
for
example, we use our
hand
to set
into
motion a
body
that
was
originally
at rest.
2.
The accelerations
imparted by
A to
B,
& and
by
B to A
are
directed
along
the
connecting
line
and
are
oppositely
oriented.
[p.
7]
3.
The ratio of accelerations
of
two mat.
p.
defines
the
ratio
of
masses. Explanation
of
the
empirical
laws involved.
B.
m
V
_
£
B
.
m.
/ik
A
One
mass can
be chosen
arbitrarily.
The
rest
of the
masses can
be derived
from it
by
experiment.
4.
The addition theorem for
accelerations.
If
one
introduces
a
vector
(x,
y, z)
that
is
equal
to
the acceleration of the
point
multiplied
by
m,
that
is,
if
one
sets
dhc
v
m
=
X

dt2
then,
for
two
masses interacting
with each
other,
this vector has
the
property
of
being
equal
for
the
two,
and of
opposite
direction.
We
call this vector
the
force
acting on
the
mass point. Thus,
this
force
always
fulfills
the condition of
equivalence
of
action and
[p. 8]
reaction.