Classical Mechanics Lecture 22
|
|
- Lucinda Franklin
- 5 years ago
- Views:
Transcription
1 Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1
2 Your Coents so the oega can stand for both the oscilla7on frequency or angular velocity right? its really confusing soe7es What does phi represent again? Also, what is the difference between angular velocity and angular frequency? They look and sound to be the sae. Who's the genius who decided oega should have two eanings? Did they run out of Greek lemers? Why don't they fly over there and get soe ore? It would probably help boost their econoy at this point. I a finding it difficult to understand how the oent of iner7a and the radius are both being used in the equa7on. Isn't the oent of iner7a dependent on the radius? Is the period propor7onal to Rc then? talking about haronic o7ons, Lets all dance "GANGNOM style ", its a perfect prac7cal exaple! Why y rooate keeps on raing Grape Fantas into y ini fridge is way ore confusing than anything that we've covered this year Can we do a potluck on Friday? Mechanics Lecture 8, Slide 2
3 Conceptual Probles workbook
4 Don t Panic!
5 I want to know why the answer to life is 42! Drill a hole through the earth and jup in what happens? Just for fun you don t need to know this.
6 I want to know why the answer to life is 42! Drill a hole through the earth and jup in what happens? You will oscillate like a ass on a spring with a period of 84 inutes. It takes 42 inutes to coe out the other side! k = g/r E Mechanics Lecture 8, Slide 5
7 I want to know why the answer to life is 42! Drill a hole through the earth and jup in what happens? You will oscillate like a ass on a spring with a period of 84 inutes. It takes 42 inutes to coe out the other side! The hole doesn t even have to go through the iddle you get the sae answer anyway as long as there is no fric7on. Mechanics Lecture 8, Slide 6
8 I want to know why the answer to life is 42! This is also the sae period of an object orbi7ng the earth right at ground level. Just for fun you don t need to know this. Mechanics Lecture 8, Slide 7
9 Panic! Is there such a thing as Rota7onal Haronic Mo7on? There bemer not be... Yes there is. Are you ready?
10 Torsion Pendulu wire τ θ I Q: In the prelecture the equa7on for restoring torque is given as τ=- κθ in clockwise direc7on..so if the restoring torque is in counter clockwise direc7ons then would τ be posi7ve? Mechanics Lecture 8, Slide 8
11 CheckPoint A torsion pendulu is used as the 7ing eleent in a clock as shown. The speed of the clock is adjusted by changing the distance of two sall disks fro the rota7on axis of the pendulu. If we adjust the disks so that they are closer to the rota7on axis, the clock runs: A) Faster B) Slower Sall disks Mechanics Lecture 8, Slide 9
12 CheckPoint If we adjust the disks so that they are closer to the rota7on axis, the clock runs A) Faster B) Slower A) The oent of iner7a decreases, so the angular frequency increases, which akes the period shorter and thus the clock faster. B) T = 2pi * sqrt(i/mgrc). If Rc decreases, T will increase, aking the clock run slower. Mechanics Lecture 8, Slide 10
13 Grading Unit 14 and 15 Ac7vity Guides will not be graded Please turn in:! Unit 14 WriMen Hoework on Monday! The Mini- labbook on your SHM or Karate Project, April 25
14 Triuf Lectures This weekend, Sat. Nov. 29! 10 a Earthquakes! 11 a Earthquake engineering snacks
15 Pendulu θ R CM For sall θ X CM Mg θ R CM X CM arc- length = R CM θ Mechanics Lecture 8, Slide 11
16 pivot The Siple Pendulu θ R CM CM θ L The siple case The general case Mechanics Lecture 8, Slide 12
17 CheckPoint If the clock is running too fast, the weight needs to be oved A) Up B) Down If the clock is running too fast then we want to reduce it's period, T, and to do that we need to increase oega, the frequency it oves with and to do that we need the posi7on of the center of ass to be further fro the pivot, which is achieved by oving the weight down. Mechanics Lecture 8, Slide 14
18 The Stick Pendulu pivot θ R CM CM M Sae period Mechanics Lecture 8, Slide 15
19 Case 1 Case 2 CheckPoint In Case 1 a s7ck of ass and length L is pivoted at one end and used as a pendulu. In Case 2 a point par7cle of ass is amached to the center of the sae s7ck. In which case is the period of the pendulu the longest? A) Case 1 B) Case 2 C) Sae C is not the right answer. Lets work through it Mechanics Lecture 8, Slide 16
20 Case 1 Case 2 In Case 1 a s7ck of ass and length L is pivoted at one end and used as a pendulu. In Case 2 a point par7cle of ass is amached to a string of length L/2? In which case is the period of the pendulu longest? A) Case 1 B) Case 2 C) Sae T = 2 s 2 3 L g T = 2 s 1 2 L g Mechanics Lecture 8, Slide 17
21 T 2 Suppose you start with 2 different pendula, one having period T 1 and the other having period T 2. T 1 T 1 > T 2 Now suppose you ake a new pendulu by hanging the first two fro the sae pivot and gluing the together. What is the period of the new pendulu? A) T 1 B) T 2 C) In between Mechanics Lecture 8, Slide 18
22 Case 1 Case 2 In Case 1 a s7ck of ass and length L is pivoted at one end and used as a pendulu. In Case 2 a point par7cle of ass is amached to the center of the sae s7ck. In which case is the period of the pendulu the longest? A) Case 1 B) Case 2 C) Sae Now lets work through it in detail Mechanics Lecture 8, Slide 19
23 Case 1 Case 2 Lets copare for each case. Mechanics Lecture 8, Slide 20
24 Case 1 Case 2 Lets copare for each case. (A) (B) (C) Mechanics Lecture 8, Slide 21
25 So we can work out Case 1 Case 2 In which case is the period longest? A) Case 1 B) Case 2 C) They are the sae Mechanics Lecture 8, Slide 22
26 The Sall Angle Approxiation θ R CM - Exact expression X CM arc- length = R CM θ % difference between θ and sinθ Angle (degrees) Mechanics Lecture 8, Slide 23
27 Clicker Question A pendulu is ade by hanging a thin hoola- hoop of diaeter D on a sall nail. What is the angular frequency of oscilla7on of the hoop for sall displaceents? (I CM = R 2 for a hoop) A) pivot (nail) B) D C) Mechanics Lecture 8, Slide 24
28 The angular frequency of oscilla7on of the hoop for sall displaceents will be given by Use parallel axis theore: I = I CM + R 2 = R 2 + R 2 = 2R 2 pivot (nail) R So X CM Mechanics Lecture 8, Slide 25
Classical Mechanics Lecture 22
Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1 Grading Unit 14 and 15 Ac7vity Guides will not be graded Please turn in:! Unit 14 WriIen
More informationClassical Mechanics Lecture 22
Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1 Grading Unit 14 and 15 Ac7vity Guides will not be graded Please turn in:! Unit 14 WriEen
More informationAnnouncements. Last year s final exam has been posted. Final exam is worth 200 points and is 2 hours: Quiz #9 this Wednesday:
Announceents sartphysics hoework deadlines have been reset to :0 PM on eceber 15 (beinnin of final exa). You can et 100% credit if you o back and correct ANY proble on the HW fro the beinnin of the seester!
More informationExam 3 Results !"#$%&%'()*+(,-./0% 123+#435%%6789:% Approximate Grade Cutoffs Ø A Ø B Ø C Ø D Ø 0 24 F
Exam 3 Results Approximate Grade Cutos Ø 75-1 A Ø 55 74 B Ø 35 54 C Ø 5 34 D Ø 4 F '$!" '#!" '!!" &!" %!" $!" #!"!"!"#$%&%'()*+(,-./% 13+#435%%6789:%!()" )('!" '!(')" ')(#!" #!(#)" #)(*!" *!(*)" *)($!"
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More informationClassical Mechanics Lecture 21
Classical Mechanics Lecture 21 Today s Concept: Simple Harmonic Mo7on: Mass on a Spring Mechanics Lecture 21, Slide 1 The Mechanical Universe, Episode 20: Harmonic Motion http://www.learner.org/vod/login.html?pid=565
More informationCHAPTER 15: Vibratory Motion
CHAPTER 15: Vibratory Motion courtesy of Richard White courtesy of Richard White 2.) 1.) Two glaring observations can be ade fro the graphic on the previous slide: 1.) The PROJECTION of a point on a circle
More informationUnit 14 Harmonic Motion. Your Comments
Today s Concepts: Periodic Motion Siple - Mass on spring Daped Forced Resonance Siple - Pendulu Unit 1, Slide 1 Your Coents Please go through the three equations for siple haronic otion and phase angle
More informationClassical Mechanics Lecture 16
Classical Mechanics Lecture 16 Today s Concepts: a) Rolling Kine6c Energy b) Angular Accelera6on Physics 211 Lecture 16, Slide 1 Thoughts from the Present & Past Can we do that cookie 6n demo again, but
More information5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page
5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks
More informationPhysics 201 Lecture 29
Phsics 1 ecture 9 Goals ecture 9 v Describe oscillator otion in a siple pendulu v Describe oscillator otion with torques v Introduce daping in SHM v Discuss resonance v Final Ea Details l Sunda, Ma 13th
More informationChapter 11. Today. Last Wednesday. Precession from Pre- lecture. Solving problems with torque
Chapter 11 Last Wednesday Solving problems with torque Work and power with torque Angular momentum Conserva5on of angular momentum Today Precession from Pre- lecture Study the condi5ons for equilibrium
More informationPHYS 1443 Section 003 Lecture #22
PHYS 443 Section 003 Lecture # Monda, Nov. 4, 003. Siple Bloc-Spring Sste. Energ of the Siple Haronic Oscillator 3. Pendulu Siple Pendulu Phsical Pendulu orsion Pendulu 4. Siple Haronic Motion and Unifor
More informationPhysics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14
Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand
More informationMore Oscillations! (Today: Harmonic Oscillators)
More Oscillations! (oday: Haronic Oscillators) Movie assignent reinder! Final due HURSDAY April 20 Subit through ecapus Different rubric; reeber to chec it even if you got 00% on your draft: http://sarahspolaor.faculty.wvu.edu/hoe/physics-0
More informationT m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω =
Thur Oct 9 Assignent 10 Mass-Spring Kineatics (x, v, a, t) Dynaics (F,, a) Tie dependence Energy Pendulu Daping and Resonances x Acos( ωt) = v = Aω sin( ωt) a = Aω cos( ωt) ω = spring k f spring = 1 k
More informationPage 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position
Physics 3: ecture Today s genda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a spring Vertical spring Energy and siple haronic otion Energy o
More informationLast Time: Finish Ch 9 Start Ch 10 Today: Chapter 10
Last Time: Finish Ch 9 Start Ch 10 Today: Chapter 10 Monday Ch 9 examples Rota:on of a rigid body Torque and angular accelera:on Today Solving problems with torque Work and power with torque Angular momentum
More informationLesson 24: Newton's Second Law (Motion)
Lesson 24: Newton's Second Law (Motion) To really appreciate Newton s Laws, it soeties helps to see how they build on each other. The First Law describes what will happen if there is no net force. The
More informationElectricity & Magnetism Lecture 13
Electricit & Magnetism Lecture 13 Toda s Concept: Torques Electricit & Magne9sm Lecture 13, Slide 1 Extra Deadlines Extra deadlines have been set up for Prelectures and Checkpoints that happened last week.
More informationm A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations
P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is.
More informationPhysics 41 HW Set 1 Chapter 15 Serway 7 th Edition
Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,
More informationLecture 16: Rotational Dynamics
Lecture 6: otational Dynamics Today s Concepts: a) olling Kine6c Energy b) Angular Accelera6on Mechanics Lecture 6, Slide I felt like every slide just had a ton of equa6ons just being used to find new
More informationSimple Harmonic Motion
Reading: Chapter 15 Siple Haronic Motion Siple Haronic Motion Frequency f Period T T 1. f Siple haronic otion x ( t) x cos( t ). Aplitude x Phase Angular frequency Since the otion returns to its initial
More information3. Period Law: Simplified proof for circular orbits Equate gravitational and centripetal forces
Physics 106 Lecture 10 Kepler s Laws and Planetary Motion-continued SJ 7 th ed.: Chap 1., 1.6 Kepler s laws of planetary otion Orbit Law Area Law Period Law Satellite and planetary orbits Orbits, potential,
More informationOSCILLATIONS AND WAVES
OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in
More informationClassical Mechanics Lecture 7
Classical Mechanics Lecture 7 Today s Concepts: Work & Kine6c Energy Mechanics Lecture 7, Slide 1 Karate Will not do Session 3 of Unit 8. It is a Karate thing. We will only mark Session 2 of unit 8. You
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More informationClassical Mechanics Lecture 7
Classical Mechanics Lecture 7 Today s Concepts: Work & Kine6c Energy Mechanics Lecture 7, Slide 1 Notices Midterm Exam Friday Feb 8 will cover stuff we do un6l today. 10 mul6ple choice + 2 problems, 2
More informationElectricity & Magnetism Lecture 3: Electric Flux and Field Lines
Electricity & Magnetism Lecture 3: Electric Flux and Field Lines Today s Concepts: A) Electric Flux B) Field Lines Gauss Law Electricity & Magne@sm Lecture 3, Slide 1 Your Comments What the heck is epsilon
More informationCHAPTER 1 MOTION & MOMENTUM
CHAPTER 1 MOTION & MOMENTUM SECTION 1 WHAT IS MOTION? All atter is constantly in MOTION Motion involves a CHANGE in position. An object changes position relative to a REFERENCE POINT. DISTANCE is the total
More informationClassical Mechanics Lecture 7
Classical Mechanics Lecture 7 UNIT 10: WORK AND ENERGY Approximate Classroom Time: Three 100 minute sessions Today s Concepts: Work & Kine6c Energy ES "Knowing is not enough; we must apply. Willing is
More informationElectricity & Magnetism Lecture 10: Kirchhoff s Rules
Electricity & Magnetism Lecture 10: Kirchhoff s Rules Today s Concept: Kirchhoff s Rules Electricity & Magne/sm Lecture 10, Slide 1 Deadline for Unit 23 Ac>vity guide and WriBen Homework is pushed to Friday
More informationChapter 11 Simple Harmonic Motion
Chapter 11 Siple Haronic Motion "We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances." Isaac Newton 11.1 Introduction to Periodic Motion
More informationPH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,
More informationOscillations: Review (Chapter 12)
Oscillations: Review (Chapter 1) Oscillations: otions that are periodic in tie (i.e. repetitive) o Swinging object (pendulu) o Vibrating object (spring, guitar string, etc.) o Part of ediu (i.e. string,
More informationPhysics 201, Lecture 15
Physics 0, Lecture 5 Today s Topics q More on Linear Moentu And Collisions Elastic and Perfect Inelastic Collision (D) Two Diensional Elastic Collisions Exercise: Billiards Board Explosion q Multi-Particle
More informationStudent Book pages
Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..
More informationNB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016
NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,
More informationClassical Mechanics Lecture 17
Classical Mechanics Lecture 17 Today s Concept: Angular Momentum Mechanics Lecture 19, Slide 1 So does L=r x p or L= Iω? Your Comments I would appreciate if I was not treated as a point par8cle, Why does
More informationParticle dynamics Physics 1A, UNSW
1 Particle dynaics Physics 1A, UNSW Newton's laws: S & J: Ch 5.1 5.9, 6.1 force, ass, acceleration also weight Physclips Chapter 5 Friction - coefficients of friction Physclips Chapter 6 Hooke's Law Dynaics
More informationNov 12, 2014 LB273 Prof. Vash6 Sawtelle. Today s Topics: SHM. h<ps:// v=6sas9n3omum&feature=youtu.be&t=16s
Nov 12, 2014 LB273 Prof. Vash6 Sawtelle Today s Topics: SHM h
More informationIn this chapter we will start the discussion on wave phenomena. We will study the following topics:
Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will study the following topics: Types of waves Aplitude, phase, frequency, period, propagation speed of a wave Mechanical
More informationUSEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta
1 USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS By: Ian Bloland, Augustana Capus, University of Alberta For: Physics Olypiad Weeend, April 6, 008, UofA Introduction: Physicists often attept to solve
More informationPhysics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015
Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section
More informationP235 Midterm Examination Prof. Cline
P235 Mier Exaination Prof. Cline THIS IS A CLOSED BOOK EXAMINATION. Do all parts of all four questions. Show all steps to get full credit. 7:00-10.00p, 30 October 2009 1:(20pts) Consider a rocket fired
More informationAnnouncements. Civil and Mechanical engineers: This week is for you!
Announcements Civil and echanical engineers: his week is for you! Ø Sta;cs: Oooh, so exci;ng! Ø Please pay aaen;on: We want you to build bridges that don t fall down! Exam 3 next Wednesday!!! (November
More informationElectricity & Magnetism Lecture 5: Electric Potential Energy
Electricity & Magnetism Lecture 5: Electric Potential Energy Today... Ø Ø Electric Poten1al Energy Unit 21 session Gravita1onal and Electrical PE Electricity & Magne/sm Lecture 5, Slide 1 Stuff you asked
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationPY241 Solutions Set 9 (Dated: November 7, 2002)
PY241 Solutions Set 9 (Dated: Noveber 7, 2002) 9-9 At what displaceent of an object undergoing siple haronic otion is the agnitude greatest for the... (a) velocity? The velocity is greatest at x = 0, the
More informationIn the session you will be divided into groups and perform four separate experiments:
Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track
More informationPHYS 1443 Section 003 Lecture #21 Wednesday, Nov. 19, 2003 Dr. Mystery Lecturer
PHYS 443 Section 003 Lecture # Wednesday, Nov. 9, 003 Dr. Mystery Lecturer. Fluid Dyanics : Flow rate and Continuity Equation. Bernoulli s Equation 3. Siple Haronic Motion 4. Siple Bloc-Spring Syste 5.
More informationTutorial Exercises: Incorporating constraints
Tutorial Exercises: Incorporating constraints 1. A siple pendulu of length l ass is suspended fro a pivot of ass M that is free to slide on a frictionless wire frae in the shape of a parabola y = ax. The
More informationA body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of
Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this
More informationElectricity & Magnetism Lecture 12
Electricity & Magnetism Lecture 12 Today s Concept: Magne2c Force on Moving Charges Electricity & Magne2sm Lecture 12, Slide 1 Today s rants I'm struggling a fair bit with this component of the course.
More informationPhysics 41 Homework #2 Chapter 16. fa. Here v is the speed of the wave. 16. The speed of a wave on a massless string would be infinite!
Physics 41 Hoewor # Chapter 1 Serway 7 th Conceptual: Q: 3,, 8, 11, 1, Probles P: 1, 3, 5, 9, 1, 5, 31, 35, 38, 4, 5, 57 Conceptual 3. (i) d=e, f, c, b, a (ii) Since, the saller the (the coefficient of
More informationAssignment 2. Tyler Shendruk October 8, Hamilton s Principle - Lagrangian and Hamiltonian dynamics.
Assignent Tyler Shendruk October 8, 010 1 Marion and Thornton Chapter 7 Hailton s Principle - Lagrangian and Hailtonian dynaics. 1.1 Proble 7.9 y z x l θ α Figure 1: A disk rolling down an incline plane.
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Torque Rotational Dynamics Current assignments Prelecture Thursday, Nov 20th at 10:30am HW#13 due this Friday at 5 pm. Clicker.1 What is the center of mass of
More information1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds)
05/07/03 HYSICS 3 Exa #1 Use g 10 /s in your calculations. NAME Feynan lease write your nae also on the back side of this exa 1. 1A A unifor thin stick of ass M 0. Kg and length 60 c is pivoted at one
More informationDepartment of Physics Preliminary Exam January 3 6, 2006
Departent of Physics Preliinary Exa January 3 6, 2006 Day 1: Classical Mechanics Tuesday, January 3, 2006 9:00 a.. 12:00 p.. Instructions: 1. Write the answer to each question on a separate sheet of paper.
More informationAnalytical Physics 1B Lecture 5: Physical Pendulums and Introduction to Mechanical Waves
Analytical Physics 1B Lecture 5: Physical Pendulums and Introduction to Mechanical Waves Sang-Wook Cheong Friday, February 16 th, 2017 Two Exam 1 Questions with errors Correct answer: L = r X p = (2000
More informationDefinition of Work, The basics
Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define
More informationHW 6 - Solutions Due November 20, 2017
Conteporary Physics I HW 6 HW 6 - Solutions Due Noveber 20, 2017 1. A 4 kg block is attached to a spring with a spring constant k 200N/, and is stretched an aount 0.2 [5 pts each]. (a) Sketch the potential
More informationAxis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis.
Instructor(s): Acosta, inzler PHYSICS DEPATMENT PHY 048, Spring 04 Final Exa March 4, 04 Nae (print, last first): Signature: On y honor, I have neither given nor received unauthorized aid on this exaination.
More informationClassical Mechanics Lecture 14
Classical Mechanics Lecture 14 Today s Concepts: a) Rota2onal Mo2on b) Moment of Iner2a Mechanics Lecture 14, Slide 1 Will we have to memorize all the different formulas for moment of iner2a? What is a
More informationElectricity & Magnetism Lecture 10: Kirchhoff s Rules
Electricity & Magnetism Lecture 10: Kirchhoff s Rules Today s Concept: Kirchhoff s Rules Electricity & Magne
More informationWileyPLUS Assignment 3. Next Week
WileyPLUS Assignent 3 Chapters 6 & 7 Due Wednesday, Noveber 11 at 11 p Next Wee No labs of tutorials Reebrance Day holiday on Wednesday (no classes) 24 Displaceent, x Mass on a spring ωt = 2π x = A cos
More informationEnergy and Momentum: The Ballistic Pendulum
Physics Departent Handout -10 Energy and Moentu: The Ballistic Pendulu The ballistic pendulu, first described in the id-eighteenth century, applies principles of echanics to the proble of easuring the
More informationAstro 7B Midterm 1 Practice Worksheet
Astro 7B Midter 1 Practice Worksheet For all the questions below, ake sure you can derive all the relevant questions that s not on the forula sheet by heart (i.e. without referring to your lecture notes).
More informationYour Comments. That s the plan
Your Comments I love physics as much as the next gal, but I was wondering. Why don't we get class off the day after an evening exam? What if the ladder has friction with the wall? Things were complicated
More informationChapter 14 Periodic Motion
Chapter 14 Periodic Motion 1 Describing Oscillation First, we want to describe the kinematical and dynamical quantities associated with Simple Harmonic Motion (SHM), for example, x, v x, a x, and F x.
More informationwhich proves the motion is simple harmonic. Now A = a 2 + b 2 = =
Worked out Exaples. The potential energy function for the force between two atos in a diatoic olecules can be expressed as follows: a U(x) = b x / x6 where a and b are positive constants and x is the distance
More informationFor a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ).
Reading: Energy 1, 2. Key concepts: Scalar products, work, kinetic energy, work-energy theore; potential energy, total energy, conservation of echanical energy, equilibriu and turning points. 1.! In 1-D
More informationChapter 14. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman. Lectures by Wayne Anderson
Chapter 14 Periodic Motion PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Exam 3 results Class Average - 57 (Approximate grade
More informationQuiz 5 PRACTICE--Ch12.1, 13.1, 14.1
Nae: Class: Date: ID: A Quiz 5 PRACTICE--Ch2., 3., 4. Multiple Choice Identify the choice that best copletes the stateent or answers the question.. A bea of light in air is incident at an angle of 35 to
More informationClassical Mechanics Lecture 20
Classical Mechanics Lecture 20 Today s Concepts: A) Angular Momentum B) Precession Mechanics Lecture 20, Slide 1 Work is of two kinds: first, altering the posi>on of ma@er at or near the earth's surface
More informationPhysics 204A FINAL EXAM Chapters 1-14 Spring 2006
Nae: Solve the following probles in the space provided Use the back of the page if needed Each proble is worth 0 points You ust show your work in a logical fashion starting with the correctly applied physical
More informationExam Results. Your scores will be posted before midnight tonight. Score Range = Approx. le<er Grade = A = B = C = D 0 34 = F
Exam Results Your scores will be posted before midnight tonight. Score Range = Approx. le
More informationProblem Set 14: Oscillations AP Physics C Supplementary Problems
Proble Set 14: Oscillations AP Physics C Suppleentary Probles 1 An oscillator consists of a bloc of ass 050 g connected to a spring When set into oscillation with aplitude 35 c, it is observed to repeat
More informationTorque and Simple Harmonic Motion
Torque and Simple Harmonic Motion Recall: Fixed Axis Rotation Angle variable Angular velocity Angular acceleration Mass element Radius of orbit Kinematics!! " d# / dt! " d 2 # / dt 2!m i Moment of inertia
More informationLast 6 lectures are easier
Your Comments I love you. Seriously. I do. And you never post it. I felt really bad whilst completing the checkpoint for this. This stuff is way above my head and I struggled with the concept of precession.
More informationVIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ]
L 1 Vibration and Waves [ ] Vibrations (oscillations) resonance pendulu springs haronic otion Waves echanical waves sound waves usical instruents VIBRATING SYSTEMS Mass and spring on air trac Mass hanging
More informationPHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1
PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque
More information= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12
Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,
More informationF = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4.
PHYSICS 151 Notes for Online Lecture.4 Springs, Strings, Pulleys, and Connected Objects Hook s Law F = 0 F = -k x 1 x = 0 x = x 1 Let s start with a horizontal spring, resting on a frictionless table.
More informationPhysics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 21 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
More informationPHYS 102 Previous Exam Problems
PHYS 102 Previous Exa Probles CHAPTER 16 Waves Transverse waves on a string Power Interference of waves Standing waves Resonance on a string 1. The displaceent of a string carrying a traveling sinusoidal
More informationSimple Harmonic Motion
Siple Haronic Motion Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and Departent of Physics, HKBU Departent of Physics Siple haronic otion In echanical physics,
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations Oscillations of a Spring Simple Harmonic Motion Energy in the Simple Harmonic Oscillator Simple Harmonic Motion Related to Uniform Circular Motion The Simple Pendulum The Physical
More information27 Oscillations: Introduction, Mass on a Spring
Chapter 7 Oscillations: Introduction, Mass on a Spring 7 Oscillations: Introduction, Mass on a Spring If a siple haronic oscillation proble does not involve the tie, you should probably be using conservation
More informationPhysics 8 Monday, October 28, 2013
Physics 8 Monday, October 28, 2013 Turn in HW8 today. I ll make them less difficult in the future! Rotation is a hard topic. And these were hard problems. HW9 (due Friday) is 7 conceptual + 8 calculation
More informationCHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1
PHYS12 Physics 1 FUNDAMENTALS Module 3 OSCILLATIONS & WAVES Text Physics by Hecht Chapter 1 OSCILLATIONS Sections: 1.5 1.6 Exaples: 1.6 1.7 1.8 1.9 CHECKLIST Haronic otion, periodic otion, siple haronic
More informationPage 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision
Physics 131: Lecture 16 Today s Agenda Elastic Collisions Definition Exaples Work and Energy Definition of work Exaples Physics 01: Lecture 10, Pg 1 Collisions Moentu is alost always consered during as
More informationPHYS 154 Practice Final Test Spring 2018
The actual test contains 10 ultiple choice questions and 2 probles. However, for extra exercise and enjoyent, this practice test includes18 questions and 4 probles. Questions: N.. ake sure that you justify
More informationPhysics 120 Final Examination
Physics 120 Final Exaination 12 August, 1998 Nae Tie: 3 hours Signature Calculator and one forula sheet allowed Student nuber Show coplete solutions to questions 3 to 8. This exaination has 8 questions.
More informationT = 2.34x10 6 s = 27.2days.
Sole the following probles in the space proided Use the back of the page if needed Each proble is worth 10 points You ust show your work in a logical fashion starting with the correctly applied and clearly
More informationLAST TIME: Simple Pendulum:
LAST TIME: Simple Pendulum: The displacement from equilibrium, x is the arclength s = L. s / L x / L Accelerating & Restoring Force in the tangential direction, taking cw as positive initial displacement
More informationClassical Mechanics Lecture 9
Classical Mechanics Lecture 9 Today's Concepts: a) Energy and Fric6on b) Poten6al energy & force Mechanics Lecture 9, Slide 1 Some comments about the course Spring examples with numbers Bring out a spring!
More information9 HOOKE S LAW AND SIMPLE HARMONIC MOTION
Experient 9 HOOKE S LAW AND SIMPLE HARMONIC MOTION Objectives 1. Verify Hoo s law,. Measure the force constant of a spring, and 3. Measure the period of oscillation of a spring-ass syste and copare it
More informationLecture 22: Harmonic Waves. Physics 2210 Fall Semester 2014
Lecture 22: Harmonic Waves Physics 2210 Fall Semester 2014 Announcements Unit 21 Simple and Physical Pendula (Nov 24th ) HW Due 11/25 th as usual No new material Wednesday November 26th. In-class discussion
More information