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Lecture 7
1
PHY121 – Physics for the Life Sciences I
Lecture 7
1. Rotational
Dynamics
: Torque
2. Newton’s Law for Rotations
3. Rotational Inertia: Moment of Inertia
Note: set your Clicker to Channel 21
2/14/2012

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*Sign up*Lecture 7
2
Recap: Newton’s Gravity
Gravitational attraction is the force acting between objects
that have a “
gravitational charge
”, i.e. gravitational mass
(one of the mysterious facts of nature is that inertial mass and gravitation charge are
proportional (or identical – in SI units) to another! This, among other facts, led Einstein to
the Theory of Relativity)
– Force of Gravity between point-masses
m
1
and
m
2
at distance
r
12
from
one another:
•
Magnitude
:
Gm
1
m
2
/
r
12
2
, INIFINTE RANGE
with
G
= 6.673×10
–11
Nm
2
/kg
2
• Direction: attractive; notation:
r
1
2
is pointing outwards
•F
o
r
SPHERICALLY SYMMETRIC
objects:
as if all mass was at center!
– e.g. on mass
m
by
M
E
of Earth at sealevel:
1
,1 on 2
1
12
2
2
2
G
mm
r
G
F
r
2
E
G
E
R
mM
G
F
j
extremely weak for
“normal” masses
2
E
E
GM
g
R
11
24
2
6
6.67 10
5.97 10
6.38 10
2
9.80m/s
m
g
j
2/14/2012

Orbital Motion around the Earth: Satellites
Satellite motion: motion of
a mass
m
around another
massive body of mass
M
…
– If only Earth gravity exits, and the orbit is
circular
(with radius
r
):
• Thus, the orbital speed is constant:
uniform circular motion!
– for a circular orbit
v =
2
π
r/T
and:
– This is a special case of Kepler’s Period Law (Kepler’s 3
rd
Law):
• The square of the orbital periods
T
2
are proportional to the 3
rd
power
of the orbital semi-major axes
a
:
2/14/2012
Lecture 7
3
2
G
F
M
G
m
r
2
23
4
Ta
GM
Net
F
2
r
m
v
M
vr
G
GM
v
r
2
r
T
2
4
Tr
GM
Note: higher
orbits
less speed !
a
m
centripetal
uniform circular motion

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*Sign up*Comparing the orbital speeds of two
satellites in different circular Earth orbits:
the higher satellite …
2/14/2012
Lecture 7
4
A.
B.
C.
14%
9%
78%
A. is faster than the satellite in
the lower orbit
B. is slower than the satellite in
the lower orbit
C. one cannot say: the speed
does not depend on the
height, but simply on the
speed of the rocket that
brought the satellite into
orbit …

Lecture 7
5
Example: Angular Kinematics
a CD player is spinning up from zero to a final (angular)
speed of
7200 rpm
, with a constant angular acceleration of
190 rad/s
2
.
Q1: How long did it take to spin up to its final speed?
– We know the final speed (
ω
f
=7200 rpm
), the initial speed (
ω
0
=0
) and the
acceleration (
α
=
190 rad/s
2
):
Q2: How many turns has it made in the first
10.0 s
?
– Two distinct periods:
– the spin-up period, lasting
3.97 s