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Chapter 11
Rotational Dynamics
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View Full Document Important quantities
∑
i
i
i
R
m
2
∑
i
i
i
v
m
∑
∑
i
i
i
i
i
m
R
m
Moment of inertia, I. Used in
τ
=I
α
. So, I
divided by timesquared has units of force
times distance (torque).
Total linear momentum is the sum
of the individual momenta.
Centerofmass is a distance. Has
to have units of meters.
Rotational Relationships
2
2
1
ϖ
α
τ
θ
I
K
I
I
L
t
t
=
=
=
∆
∆
=
∆
∆
=
Position
Velocity
Acceleration
Momentum
Force/Torque
Kinetic Energy
t
t
t
+
=
+
+
=
0
2
0
2
1
Master equations:
Onetoone
correspondence of
rotational equations to
linear equations.
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View Full Document Torque
( 29
( 29
( 29
α
τ
I
mr
r
r
m
r
ma
Fr
=
=
=
=
=
2
Force and Torque Combined: What is the acceleration of a
pulley with a nonzero moment of inertia?
R
a
I
I
TR
R
a
TR
I
=
=
=
=
=
α
τ
Torque relation for pulley:
ma
T
mg
=

Force Relation for Mass
Put it together:
+
=
=
=

2
2
1
mR
I
ma
mg
R
a
I
T
ma
T
mg
+
=
2
1
1
mR
I
g
a
NOTE: Positive down!
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View Full Document How high does it go?
Use energy conservation.
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This note was uploaded on 08/16/2011 for the course PHY 2053 taught by Professor Vellaris during the Fall '08 term at University of Central Florida.
 Fall '08
 Vellaris
 Physics, Force, Inertia, Momentum

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