Your Comments

1. Your Comments So I actually watched the video and did the prelecture questions this time....ikinda 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.

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

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 !!

4. “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

5. Why 42 ?? Drill a hole through the earth and jump in – what happens? Just for fun – you don’t need to know this.

6. Drill a hole through the earth and jump in – what happens? You will oscillate like a mass on a spring with a period of 84 minutes. It takes 42 minutesto come out the other side! k = mg/RE

7. Drill a hole through the earth and jump in – what happens? You will oscillate like a mass on a spring with a period of 84 minutes. It takes 42 minutesto come out the other side! The hole doesn’t even have to go through the middle – you get the same answer anyway (as long as there is no friction).

8. This is also the same period of an object orbiting the earth right at ground level. Just for fun – you don’t need to know this.

9. Physics 211Lecture 22 Today’s Concept: Simple Harmonic Motion: Motion of a Pendulum

10. Torsion Pendulum “If it wasn't a toy or found on a playground, I have trouble conceptually understanding it. Please explain a torsion pendulum..” wire   I “Can you explain the difference between angular frequency and angular velocity again?”

11. CheckPoint 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 “My grandma has a torsion pendulum clock!”

12. CheckPoint 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..

13. Pendulum RCM q Forsmall q XCM Mg RCM q XCM arc-length=RCMq

14. The Simple Pendulum The simple case q L pivot RCM q CM “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)?”

15. CheckPoint 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

16. 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.

17. The Stick Pendulum pivot RCM q CM M Same period Demo

18. CheckPoint 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 C is not the right answer. Lets work through it

19. 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

20. m m Suppose you start with 2 different pendula, one having period T1 and the other having period T2. T2 T1>T2 T1 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

21. 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 Now lets work through it in detail

22. Case 2 Case 1 m m Lets compare for each case. m

23. Case 2 Case 1 m m Lets compare for each case. m (A) (B) (C)

24. So we can work out Case 2 Case 1 m m m In which case is the period longest (i.e. w smallest)? A) Case 1 B) Case 2 C) They are the same Same period

25. The Small Angle Approximation “Can we go over the "small angle" ordeal? Why can't we use the sin(theta)in our equation?” % difference between qand sinq RCM q Angle (degrees) XCM arc-length=RCMq

26. Clicker Question 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=mR2for a hoop) pivot (nail) A) B) C) R D

27. Clicker Question 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? pivot (nail) A) B) C) D

28. 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 So m