Physics 211 Lecture 22, Slide 1

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Physics 211 Lecture 22
Today's Concepts Simple Harmonic Motion Motion
of a Pendulum
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Is the final going to be evenly divided into the
various topics throughout the course or will it
focus on the newer material? The lack of a
prelecture. I'm like a lost soul out in the
wilderness with nothing but the cruel sun to beat
down upon me. Woe is me! Will I never know the
true nature of the pendulum? Excuse me while I
cry in the corner. im disappointed that the
pre-lecture is not ready...they really help me
understand I don't know why, but angular anything
seems confusing to me. I'm not sure how we
determine if we're supposed to use sin or
cos. Can we postpone one of the homework
assignments until next week if at least 85 of us
get the clicker questions right? HOW MUCH MORE DO
WE HAVE TO LEARN?! The part about our final being
at 8am. What is up with that? I mean, can't we
just have it at night like our hour exams? Or in
the afternoon? Why my roommate keeps on ramming
Grape Fantas into my mini fridge is way more
confusing than anything that we've covered this
year So this neutron walks into a bar and asks,
"How much for a drink?" The bartender replies,
"For you, no charge."
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Torsion Pendulum
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Preflight
A torsion pendulum is used as the timing element
in a clock as shown. The speed of the clock is
adjusted by changing the distance of two small
disks from the rotation axis of the pendulum. If
we adjust the disks so that they are closer to
the rotation axis, the clock runs A) Faster
B) Slower
Small disks
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If we adjust the disks so that they are closer to
the rotation axis, the clock runs A) Faster
B) Slower
A) The moment of inertia decreases, so the
angular frequency increases, which makes the
period shorter and thus the clock faster.
B) Smaller moment of inertia means it takes less
torque to turn the pendulum and results in a
shorter period..
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Pendulum
pivot
Rcm
q
cm
Forsmall q
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The Simple Pendulum
pivot
q
Rcm
cm
M
The general case
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Preflight
A simple pendulum is used as the timing element
in a clock as shown. An adjustment screw is used
to make the pendulum shorter (longer) by moving
the weight up (down) along the shaft that
connects it to the pivot. If the clock is
running too fast, the weight needs to be moved
A) Up B) Down
Adjustment screw
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If the clock is running too fast, the weight
needs to be moved A) Up B) Down
A) since T (L/G)1/2 decreasing the length will
shorten the period.
B) The longer the length of a pendulum, the
longer the period.
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The Stick Pendulum
pivot
Rcm
q
cm
M
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Preflight
Case 1
Case 2
In Case 1 a stick of mass m and length L is
pivoted at one end and used as a pendulum. In
Case 2 a point particle of mass m is attached to
the center of the same stick. In which case is
the period of the pendulum the longest? A) Case
1 B) Case 2 C) Same
m
m
m
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Case 1
Case 2
In Case 1 a stick of mass m and length L is
pivoted at one end and used as a pendulum. In
Case 2 a point particle of mass m is attached to
a string of length L/2? In which case is the
period of the pendulum longest? A) Case 1 B)
Case 2 C) Same
m
m
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Suppose you start with 2 different pendula, one
having period T1 and the other having period T2.
T1 gt T2
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Case 1
Case 2
In Case 1 a stick of mass m and length L is
pivoted at one end and used as a pendulum. In
Case 2 a point particle of mass m is attached to
the center of the same stick. In which case is
the period of the pendulum the longest? A) Case
1 B) Case 2 C) Same
m
m
m
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m
m
m
16
m
m
m
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So we can work out
Case 2
Case 1
m
m
m

• In which case is the period longest?
• Case 1
• Case 2
• They are the same

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The small angle approximation
- Exact expression
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Act
A pendulum is made by hanging a thin hoola-hoop
of diameter D on a small nail. What is the
angular frequency of oscillation of the hoop for
small displacements? (ICM mR2 for a hoop)
pivot (nail)
(A) (B) (C)
D
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The angular frequency of oscillation of the hoop
for small displacements will be given by
Use parallel axis theorem I Icm mR2
mR2 mR2 2mR2
pivot (nail)
R
x cm
m