4
DOC.
1
MECHANICS
LECTURE NOTES
[p. 5]
Tangential
and Normal
Acceleration
There
exists
a
particularly noteworthy
way
of
resolving
the
acceleration
vector
into
components,
namely,
the resolution into
a
tangential
and
into
a
normal
component.
N
=
dv
dt
T
=
v
P
Direction
cos
of
N:
a ß y
Direction
cos
of
tangt
a'
ß' y'
d2x
dv
v2
~j7T
=
a
^-
+
a
- dt2 dt
p
[8]
[p. 6]
B.
Dynamics
of
the
Material
P.[9]
1. Galileo's principle
of inertia
a
m.p.
that
is
present
alone
in
space
not
acted
upon
by
other
bodies[10]
moves
without acceleration.
(a)
In
a
certain
sense,
this law
is
an
empirical law;
(billiard ball,
railway
car).
Strictly
speaking,
however,
it has
the character of
a
definition.
For
we say
that other
bodies do
not act
on a
body
if
this
body moves uniformly
in
a
straight
line. But for all
practical
purposes
the
law
can
be
designated as
empirical,
because
experience happens
to be such
that the
law
can
be
carried
out
or
maintained without
any artificial-looking assump-
tions.[11]