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]