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Lecture 32
Midterm 4
Wednesday Nov 19
Topics:
Rotation
Center of mass
Angular momentum
Gravitation
Chapter 13
Universal Gravitation
Homework 10
Chapter 11 (angular momentum)
Q 9,13
P 21,29
Chapter 13
Q 2,10
P 33

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*Sign up* Newton’s Law of Universal
Gravitation
z
Every particle in the Universe
attracts every other particle
with a force that is directly
proportional to the product of
their masses and inversely
proportional to the distance
between them
z
G
is the
universal
gravitational constant
and
equals 6.673 x 10
-11
N
⋅
m
2
/ kg
2
12
2
g
mm
FG
r
=

Law of Gravitation, cont
z
This is an example of an
inverse square law
z
The magnitude of the force varies as the inverse
square of the separation of the particles
z
The law can also be expressed in vector form
z
The negative sign indicates an attractive force
12
12
12
2
ˆ
mm
G
r
=−
Fr
r

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*Sign up* Notation
z
is the force exerted by particle 1 on
particle 2
z
The negative sign in the vector form of the
equation indicates that particle 2 is attracted
toward particle 1
z
is the force exerted by particle 2 on
particle 1
12
F
r
21
F
r

More About Forces
z
z
The forces form a Newton’s
Third Law action-reaction
pair
z
Gravitation is a field force
that always exists between
two particles, regardless of
the medium between them
z
The force decreases rapidly
as distance increases
z
A consequence of the
inverse square law
12
21
=−
FF
rr

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*Sign up* Gravitational Force Due to a
Distribution of Mass
z
The gravitational force exerted by a finite-
size, spherically symmetric mass distribution
on a particle outside the distribution is the
same as if the entire mass of the distribution
were concentrated at the center
z
The force exerted by the Earth on a particle
of mass m near the surface of the Earth is
2
E
g
E
Mm
FG
R
=

G vs. g
z
Always distinguish between
G
and
g
z
G
is the universal gravitational constant
z
It is the same everywhere
z
g
is the acceleration due to gravity
z
g
= 9.80 m/s
2
at the surface of the Earth
z
g
will vary by location

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*Sign up* Finding
g
from
G
z
The magnitude of the force acting on an object
of mass
m
in freefall near the Earth’s surface is
mg
z
This can be set equal to the force of universal
gravitation acting on the object
2
2
E
E
E
E
Mm
mg
G
R
M
gG
R
=
=

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