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MA 36600 LECTURE NOTES: MONDAY, JANUARY 12
Say that we have an object of mass
m
, perhaps measured in kilograms. Also, say that
x
=
x
(
t
)isthe
position of an object, perhaps measured in meters, at time
t
, perhaps measured in seconds. Then
v
=
dx
dt
=˙
x
is the velocity measured in meters/second, and
a
=
dv
dt
=
d
2
x
dt
2
=¨
x
is the acceleration measured in meters/second
2
. Moreover,
F
denotes the total force on an object, so the
expression “
F
=
ma
” really means
“
m
d
2
x
dt
2
= the sum of the forces on the object.”
This is called
Newton’s Second Law of Motion
. Hence
F
=
ma
is really a diFerential equation in disguise.
Gravity and Air Resistance.
We give more speci±c examples. Say that we have a binary system i.e. a
system consisting of two objects which are attracted to each other by gravity. Newton discovered that
“any body with mass
M
attracts any other body with mass
m
directly toward the mass
M
,
with a magnitude proportional to the (product of the two) masses and inversely proportional
to the square of the distance separating them.”
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.
 Spring '09
 EdrayGoins

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