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So I actually watched the video and did the prelecture questions this time....i kinda get it, but lets hope you're right and i understand this section better tomorrow!The derivations were a bit intimidating at first, but after a moment of re-analyzing the equations, the process and formulas made (for the most part) sense.Pretty simple, just plug and chug for the most partHow to get a date: Girl, you must be sin(pi/2), because you are the 1. Works every time.3 things: 1) We're nearing the end of the semester. 2) I love physics. 3) I haven't had a comment up even once. Negate one of the three statements(except the first two), pretty please?I actually understood everything very well, because I did this so early when I could actually take the time to understand it. The Stanley Cup playoffs should be on all the time...it motivated me to get this done before they started on Wednesday. Go Blackhawks! :DCan we discuss the physics behind Star Trek? Please? I feel like the guy from office space now..... I'm totally hypnotized into not caring about physics, life, college, etc. Let's go destroy a copy machine!While watching these videos, the constant pendulum motions hypnotized me and I passed out. When I finally came to, I was in the Loomis basement strapped to a table with an axe blade on a thin rod oscillating over my head. A hooded figure told me to determine the angle of the oscillation before I was beheaded. When I asked if he accounted for air resistance and friction, he let me go.
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Mechanics Lecture 8, Slide 1
Mechanics Lecture 8, Slide 2
“Physics makes me feel dumb. Why make such simple things as a ball swinging on a string so difficult?!”
Mechanics Lecture 17, Slide 3
3rd Exam is next Wednesday at 7pm:Covers lectures 14-20 (not the stuff we are doing today)
Sign up for the conflict if you need to before the end of this week. As before, email Dr. Jain if you have a double conflict (rdjain1@illinois.edu).
Next Tuesdays class will be a review (Fall 2010 exam) .
Don’t forget about office hours !!
“There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it
will instantly disappear and be replaced by something even more bizarre and inexplicable.”
“There is another theory which states that this has already happened.”
Douglas Adams
Mechanics Lecture 8, Slide 4
Drill a hole through the earth and jump in – what happens?
Just for fun – you don’t need to know this.
Why 42 ??
You will oscillate like a mass on a spring with a period of 84 minutes. It takes 42 minutes to come out the other side!
Drill a hole through the earth and jump in – what happens?
k = mg/RE
Mechanics Lecture 8, Slide 6
The hole doesn’t even have to go through the middle – you get the same answer anyway (as long as there is no friction).
Mechanics Lecture 8, Slide 7
You will oscillate like a mass on a spring with a period of 84 minutes. It takes 42 minutes to come out the other side!
Drill a hole through the earth and jump in – what happens?
This is also the same period of an object orbiting the earth right at ground level.
Mechanics Lecture 8, Slide 8Just for fun – you don’t need to know this.
Physics 211Lecture 22
Today’s Concept:Simple Harmonic Motion: Motion of a Pendulum
Mechanics Lecture 8, Slide 9
I
wire
Torsion Pendulum
“If it wasn't a toy or found on a playground, I have trouble conceptually understanding it. Please explain a torsion pendulum..”
I
2
2
dI
dt
)cos()( max tt
22
2
d
dt
I
Mechanics Lecture 8, Slide 10
“Can you explain the difference between angular frequency and angular velocity again?”
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
CheckPoint
Mechanics Lecture 8, Slide 11
“My grandma has a torsion pendulum clock!”
If we adjust the disks so that they are closer to the rotation axis, the clock runs
A) Faster B) Slower
I decreases, so the angular f increases. period shorter, the clock faster..
I
Mechanics Lecture 8, Slide 12
CheckPoint
Pendulum
I
2
2
dt
dI
22
2
d
dt
q
CMMgXXCM
RCM
Mg
q
arc-length = RCM q
XCM
RCM
Mechanics Lecture 8, Slide 13
I
MgRCM
Forsmall q
CMMgR
I
MgR
dt
d CM2
2
CM
pivot
q
RCM
The Simple Pendulum
2
MgL
ML
g
L
qL
The simple case
Mechanics Lecture 8, Slide 14
I
MgRCM
“what is the difference between a simple pedulem and a physical pedulem. mathematically?”“Can we discuss the differences between a simple pendulum and a physical pendulum. How would the two compare if they both had equal lengths (like in the Pre-lecture Question)?”
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
CheckPoint
Mechanics Lecture 8, Slide 15
If the clock is running too fast, the weight needs to be moved A) Up B) Down
Because angular frequency is inversely proportional to length, the pendulum will swing slower if the rod is moved down because the length will be increased.
L
g
Mechanics Lecture 8, Slide 16
CheckPoint
M
pivot
qRCM
The Stick Pendulum
L
g
32
2
L
2
3
1ML
Same period
2
3L
L
CM
Mechanics Lecture 8, Slide 17
I
MgRCM
Demo
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
Case 1 Case 2
C is not the right answer.
Lets work through it
CheckPoint
m
m
m
Mechanics Lecture 8, Slide 18
L
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
Case 1 Case 2
L
g
32
12
g
L
1
2L
m
Mechanics Lecture 8, Slide 19
Now suppose you make a new pendulum by hanging the first two from the same pivot and gluing them together.
What is the period of the new pendulum?
A) T1 B) T2 C) In between
m
Suppose you start with 2 different pendula, one having period T1 and the other having period T2.
T1
T2
T1 > T2
Mechanics Lecture 8, Slide 20
mm
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
Now lets work through it in detail
Case 1 Case 2
m
m
m
Mechanics Lecture 8, Slide 21
(A)
(B)
(C)
222
3
4
3
1mLmLmL
222
6
5
2
1
3
1mLmLmL
22
2
12
7
23
1mL
LmmL
Case 2m
m
2
3
1mL
mCase 1
Lets compare for each case.
Mechanics Lecture 8, Slide 23
I
MgRCM
In which case is the period longest (i.e. w smallest)?
A) Case 1
B) Case 2
C) They are the same
m
Case 1
So we can work out I
MgRCM
L
g
32
L
g
127
Case 2
m
m
Mechanics Lecture 8, Slide 24
Same period
2
3L
L
Angle (degrees)
% d
iffer
ence
bet
wee
n q
and
sin
q
The Small Angle Approximation
q
arc-length = RCM q
XCM
RCM
sin2
2
2
dt
d
...5040
1
120
1
6
1...
!7
1
!5
1
!3
1sin 753753
Mechanics Lecture 8, Slide 25
“Can we go over the "small angle" ordeal? Why can't we use the sin(theta)in our equation?”
A pendulum is made by hanging a thin hoola-hoop of radius R on a small nail. What is the moment of inertia of the hoop about an axis through the nail? (Recall that ICM = mR2 for a hoop)
A)
B)
C)
D
pivot (nail)
Clicker Question
2mRI
Mechanics Lecture 8, Slide 26
R22mRI
24mRI
A pendulum is made by hanging a thin hoola-hoop of radius R on a small nail. What is the angular frequency of oscillation of the hoop for small displacements?
A)
B)
C)
D
pivot (nail)
Clicker Question
R
g
2
R
g2
R
g2
Mechanics Lecture 8, Slide 27
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