So I actually watched the video and did the prelecture questions this time....i kinda get it, but...

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


“Physics makes me feel dumb. Why make such simple things as a ball swinging on a string so difficult?!”


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 ([email protected]).

Next Tuesdays class will be a review (Fall 2010 exam) .

Don’t forget about office hours !!

mailto:[email protected]?subject=Physics%20211

“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


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!


k = mg/RE


The hole doesn’t even have to go through the middle – you get the same answer anyway (as long as there is no friction).


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!


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


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


“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


“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


CheckPoint

Pendulum

I

2

2

dt

dI

22

2

d

dt

q

CMMgXXCM

RCM

Mg

q

arc-length = RCM q

XCM

RCM


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


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


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


CheckPoint

M

pivot

qRCM

The Stick Pendulum

L

g

32

2

L

2

3

1ML

Same period

2

3L

L

CM


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


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?


Case 1 Case 2

L

g

32

12

g

L

1

2L

m


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


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?


Now lets work through it in detail

Case 1 Case 2

m

m

m


2

Lmg

Case 2m

m

mCase 1

I

MgRCMLets compare for each case.


22

Lmg

(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.


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


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


“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


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


The angular frequency of oscillation of the hoop for small

displacements will be given by

R X

CM

Use parallel axis theorem: I = ICM + mR2

m

= mR2 + mR2 = 2mR2

pivot (nail)

22 2

mgR g g

mR R D


Sog

D

I

mgRCM

So I actually watched the video and did the prelecture questions this time....i kinda get it, but...

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