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Physics 207 – Lecture 12
Physics 207: Lecture 16, Pg 1
Physics 207,
Physics 207,
Lecture 16, Oct. 29
Lecture 16, Oct. 29
Agenda: Chapter 13
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Center of Mass
Center of Mass
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Torque
Torque
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Moment of Inertia
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Rotational Energy
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Rotational Momentum
Assignment:
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Wednesday is an exam review session, Exam will be
held in rooms B102 &
held in rooms B102 & B130 in Van Vleck at 7:15 PM
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MP Homework 7, Ch. 11, 5 problems,
MP Homework 7, Ch. 11, 5 problems,
NOTE:
Due Wednesday at 4 PM
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MP Homework 7A, Ch. 13, 5 problems, available soon
Physics 207: Lecture 16, Pg 2
Chap. 13: Rotational Dynamics
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Up until now rotation has been only in terms of circular
motion with a
c
= v
2
/ R
and  a
T
 = d v  / dt
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Rotation is common in the world around us.
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Many ideas developed for translational motion are
transferable.
Physics 207: Lecture 16, Pg 3
Conservation of angular momentum has consequences
How does one describe rotation (magnitude and direction)?
Physics 207: Lecture 16, Pg 4
Rotational Dynamics: A child
Rotational Dynamics: A child’
s toy, a physics
playground or a student
playground or a student’
s nightmare
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A merrygoround is spinning and we run and
jump on it.
What does it do?
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We are standing on the rim and our “friends”
spin it faster. What happens to us?
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We are standing on the rim a walk towards
the center.
Does anything change?
Physics 207: Lecture 16, Pg 5
Rotational Variables
Rotational Variables
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Rotation about a fixed axis:
xrhombus
Consider a disk rotating about
an axis through its center:]
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How do we describe the motion:
(Analogous to the linear case
)
ϖ
θ
R
(rad/s)
2
Tangential
v
T
dt
d
=
=
=
π
θ
ϖ
dt
dx
=
v
Physics 207: Lecture 16, Pg 6
Rotational Variables...
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Recall: At a point a distance
R
away from the axis of
rotation, the tangential motion:
xrhombus
x =
θ
R
xrhombus
v =
ϖ
R
xrhombus
a =
α
R
ϖ
α
R
v =
ϖ
R
x
θ
rad)
in
position
(angular
2
1
rad/s)
in
elocity
(angular v
)
rad/s
in
accelation
(angular
constant
2
0
0
0
2
t
t
t
α
ϖ
θ
θ
α
ϖ
ϖ
α
+
+
=
+
=
=
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Physics 207 – Lecture 12
Physics 207: Lecture 16, Pg 7
Summary
(with comparison to 1
(with comparison to 1
D kinematics)
Angular
Linear
constant
=
α
ϖ
=
ϖ
0
+
α
t
θ
θ
ϖ
α
=
+
+
0
0
2
1
2
t
t
constant
=
a
at
+
=
0
v
v
2
0
0
2
1
v
at
t
x
x
+
+
=
And for a point at a distance
R
from the rotation axis:
x = R
θ
v =
ϖ
R
a =
α
R
Physics 207: Lecture 16, Pg 9
Lecture 15,
Lecture 15,
Exercise 5
Exercise 5
Rotational Definitions
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A goofy friend sees a disk spinning and says “Ooh,
look! There’s a wheel with a negative
ϖ
and with
antiparallel
ϖ
and
α
!”
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Which of the following is a true statement about the
wheel?
(A)
(A) The wheel is spinning counterclockwise and slowing down.
(B)
(B) The wheel is spinning counterclockwise and speeding up.
(C)
(C) The wheel is spinning clockwise and slowing down.
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 Spring '06
 Winnokur
 Physics, Angular Momentum, Center Of Mass, Energy, Inertia, Mass, Momentum, Moment Of Inertia, Rigid Body, Rotation

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