Moment of Inertia. Terminology. Definitions Moment of inertia of a body with mass, m, about the x axis: Transfer Theorem - 1. ( )dm. = y 2 + z 2.
|
|
- Theodora Maud Hensley
- 6 years ago
- Views:
Transcription
1 Terinology Moent of Inertia ME 202 Moent of inertia (MOI) = second ass oent Instead of ultiplying ass by distance to the first power (which gives the first ass oent), we ultiply it by distance to the second power. 2 Definitions Moent of inertia of a body with ass,, about the x axis: ( )d I x = y 2 + z 2 Moent of inertia of a body with ass,, about the y axis: ( )d I y = x 2 + z 2 Moent of inertia of a body with ass,, about the z axis: ( )d = x 2 + y 2 3 Transfer Theore - 1 We can transfer the oent of inertia fro one axis to another, provided that the two axes are parallel. In other words, if we know the oent of inertia about one axis, we can copute it about any other axis parallel to the first axis. 4
2 Transfer Theore - 2 If the oent of inertia of a body with ass about an axis x through the ass center is I G x, and the perpendicular distance fro the x axis to the (parallel) axis x is d, then the oent of inertia of the body about the x axis is I x = I G x + d! 2 transfer ter Transfer Theore - 3 The oent of inertia to which the transfer ter is added is always the one for an axis through the ass center. The oent of inertia about an axis through the ass center is saller than the oent of inertia about any other parallel axis. 5 6 Transfer Theore - 4 We can transfer fro any axis to a parallel axis through the ass center by subtracting the transfer ter. I G x = I x d 2 Radius of Gyration The radius of gyration about the x axis is denoted by. k x ( )d I x = y 2 + z 2 By definition, the radius of gyration of a ass about the x axis is k x = I x = k x 2 7 8
3 Coposite Masses Since the oent of inertia is an integral, and since the integral over a su of several asses equals the su of the integrals over the individual asses, we can find the oent inertia of a coposite ass by adding the oents of inertia of its parts. (Regions with no ass can be subtracted.) γ lb / ft For a straight, slender, unifor bar: I G = 1 12 L2 I A = I G + d 2 Find IA (about the axis through A that is noral to the plane of the figure). Into how any parts should we divide the structure? Use two bars, each with length I A = 1 12 L2 + L 2 2 L ft L2 + 2L = L = γ L g L2 36 I A 1 γ L 3 36 g 1 ( 3 lb / ft) ( 3 ft) 3 = 2.17 slug ft ft / sec For a right, unifor, circular cone: I G 10 r 2 = ρv V = 1 3 πr 2 h Find Iz. Into how any parts should we divide the structure? 11 ρ = 200 kg / 3 Is the issing peak the sae size as the hole? h peak 200 = h peak = Use three parts: large, full cone; sall issing peak of large cone; hole. = I large I peak I hole 10 large R peak r hole r 2 ρ = 200 kg / 3 10 large R peak r hole r 2 12 For a right, unifor, circular cone: I G 10 r 2 = ρv ( ) 10 ρ V large R2 V peak r 2 V hole r 2 ( ) = π 10 ρ R4 h large r 4 h peak r 4 h hole ( ) = π 10 ρ R4 h large r 4 h peak + h hole V = 1 3 πr 2 h
4 ρ = 200 kg / 3 ( ) = π 10 ρ R4 h large r 4 h peak + h hole = π ( 200 kg / 3) kg 2 ( ) ( ) Rod: 3 kg/ Plate with hole: 12 kg/ 2 Find IG (about an axis noral to the plane of the figure). First, find G. Second, copute the MOI. Into how any parts should we divide the structure? Three pieces: two rods and one plate
5 Moent of Inertia 2 Although the FMM is a vector, the MOI is not. Mass and the square of a distance are both scalars. The diensions of the MOI are ass ties the square of length. Typical units are slug ties foot squared or kilogra ties eter squared. 3 In these integrals, each eleent of ass, d, is ultiplied by the square of its distance fro the axis about which the MOI is coputed. Results of these integrals depend on the shape of the body and the distribution of the ass within it. For a body with what is called spherical syetry, all three of the MOI are equal. A unifor sphere and a unifor cube are both aong the bodies that have spherical syetry. 4 Coputing the MOI using the integrals on the previous slide can be tedious. But any books contain tables showing the MOI for various three-diensional bodies. The MOI are typically given about three perpendicular axes that pass through the bodies ass centers. The transfer theore (aka the parallel axis theore) akes it easy to use the result fro a table to copute the MOI about an axis that does not pass through a body s ass center but is parallel to an axis for which the MOI is given in the table. 5 You should eorize this equation. And you should understand that it can be used between any two parallel axes, provided that one of the passes through the ass center of the body in question. Page 1 of 4
6 6 You should eorize the fact that the MOI about a given axis through the ass center is the sallest MOI that can be coputed for any axis parallel to the given axis. 7 This is siply a rearrangeent of the equation on slide 5, showing how to use the transfer theore to copute the MOI about an axis through the ass center when we already know the MOI about a parallel axis that does not pass through the ass center. 8 The position of a body s ass center is where we would find all of the body s ass if we considered the body to be a particle. In a siilar way, the radius of gyration is where we would find all of the body s ass if we considered the body to be an infinitely thin cylinder with radius k. For the MOI about the x axis, the cylinder would be parallel to and centered on the x axis. Since all of the cylinder s ass would be at the sae distance fro the axis, the squared distance in the first integral on slide 3 is the radius of gyration and can be taken outside the integral. That leads to the final equation on this slide. If we have any two of the quantities ass, radius of gyration and MOI, we can copute the third using this definition. 9 Because a MOI is an integral, the techniques used to locate a body s ass center or to copute the FMM for a body ade up of several siple shapes can also be applied to copute the body s MOI. The MOI of a hole can be subtracted. But adding and subtracting are correct only when all of the MOI of the body s pieces are coputed about the sae axis. Page 2 of 4
7 10 We cannot account for the exact shape of the region where the rods intersect, because we have no inforation about that. Two equations are needed for this calculation. One is the MOI for a thin, unifor rod about an axis perpendicular to the rod and passing through the rod s ass center. The other equation is the parallel axis theore. Each rod s MOI is coputed using the two equations, and the two MOI are added. Note that the ass of each rod is its weight per unit length divided by g and ultiplied by L. In the final equation, we ust expand the lb unit to slug-ft/sec 2 before siplifying. 11 A siple calculation shows that the conical hole is not the sae size as the issing peak of the larger cone. Forulas for a right, circular cone can be found in books or at web sites. In the final equation, the radius of the base of the large cone is denoted by R, and the radius of the bases of the issing peak and hole is denoted by r. It reains to substitute for the asses and volues, siplify and copute. These operations are shown on the next two slides. 12 The final equation shows that each ter is proportional to the fourth power of a radius. 13 This is the nuerical result for the final equation fro the previous slide. Page 3 of 4
8 14 For any coposite shapes, it is necessary to find the ass center before coputing the MOI. If the ass center s location were known, it would be a siple atter to transfer the MOI for each piece of the body to the ass center. But in transferring the MOI for each piece to the body s overall ass center, the transfer distance depends on the location of the ass center. Because the location is not given, we ust first find it. That requires that we copute the FMM of each piece relative to a coon point, add the FMM and divide by the total ass. Page 4 of 4
Subject Code: R13110/R13 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS
Set No - 1 I B. Tech I Seester Regular Exainations Jan./Feb. 2015 ENGINEERING MECHANICS (Coon to CE, ME, CSE, PCE, IT, Che E, Aero E, AME, Min E, PE, Metal E) Tie: 3 hours Max. Marks: 70 What is the principle
More informationIntroduction to Robotics (CS223A) (Winter 2006/2007) Homework #5 solutions
Introduction to Robotics (CS3A) Handout (Winter 6/7) Hoework #5 solutions. (a) Derive a forula that transfors an inertia tensor given in soe frae {C} into a new frae {A}. The frae {A} can differ fro frae
More informationProblem T1. Main sequence stars (11 points)
Proble T1. Main sequence stars 11 points Part. Lifetie of Sun points i..7 pts Since the Sun behaves as a perfectly black body it s total radiation power can be expressed fro the Stefan- Boltzann law as
More informationName: Partner(s): Date: Angular Momentum
Nae: Partner(s): Date: Angular Moentu 1. Purpose: In this lab, you will use the principle of conservation of angular oentu to easure the oent of inertia of various objects. Additionally, you develop a
More informationU V. r In Uniform Field the Potential Difference is V Ed
SPHI/W nit 7.8 Electric Potential Page of 5 Notes Physics Tool box Electric Potential Energy the electric potential energy stored in a syste k of two charges and is E r k Coulobs Constant is N C 9 9. E
More informationChapter Torque equals the diver s weight x distance from the pivot. List your variables and solve for distance.
Chapter 9 1. Put F 1 along the x axis. Add the three y-coponents (which total 0) and solve for the y- coponent of F 3. Now add the x-coponents of all three vectors (which total 0) and solve for the x-coponent
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 information2.003 Engineering Dynamics Problem Set 2 Solutions
.003 Engineering Dynaics Proble Set Solutions This proble set is priarily eant to give the student practice in describing otion. This is the subject of kineatics. It is strongly recoended that you study
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 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 informationThe Weierstrass Approximation Theorem
36 The Weierstrass Approxiation Theore Recall that the fundaental idea underlying the construction of the real nubers is approxiation by the sipler rational nubers. Firstly, nubers are often deterined
More informationPY /005 Practice Test 1, 2004 Feb. 10
PY 205-004/005 Practice Test 1, 2004 Feb. 10 Print nae Lab section I have neither given nor received unauthorized aid on this test. Sign ature: When you turn in the test (including forula page) you ust
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.it.edu 8.012 Physics I: Classical Mechanics Fall 2008 For inforation about citing these aterials or our Ters of Use, isit: http://ocw.it.edu/ters. MASSACHUSETTS INSTITUTE
More informationChemistry 432 Problem Set 11 Spring 2018 Solutions
1. Show that for an ideal gas Cheistry 432 Proble Set 11 Spring 2018 Solutions P V 2 3 < KE > where is the average kinetic energy of the gas olecules. P 1 3 ρ v2 KE 1 2 v2 ρ N V P V 1 3 N v2 2 3 N
More informationPotential Energy 4/7/11. Lecture 22: Chapter 11 Gravity Lecture 2. Gravitational potential energy. Total energy. Apollo 14, at lift-off
Lecture 22: Chapter 11 Gravity Lecture 2 2 Potential Energy r Gravitational potential energy Escape velocity of a point ass for ass distributions Discrete Rod Spherical shell Sphere Gravitational potential
More informationNAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%
NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity
More informationa a a a a a a m a b a b
Algebra / Trig Final Exa Study Guide (Fall Seester) Moncada/Dunphy Inforation About the Final Exa The final exa is cuulative, covering Appendix A (A.1-A.5) and Chapter 1. All probles will be ultiple choice
More informationOcean 420 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers
Ocean 40 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers 1. Hydrostatic Balance a) Set all of the levels on one of the coluns to the lowest possible density.
More informationThe Hydrogen Atom. Nucleus charge +Ze mass m 1 coordinates x 1, y 1, z 1. Electron charge e mass m 2 coordinates x 2, y 2, z 2
The Hydrogen Ato The only ato that can be solved exactly. The results becoe the basis for understanding all other atos and olecules. Orbital Angular Moentu Spherical Haronics Nucleus charge +Ze ass coordinates
More informationPhysics 139B Solutions to Homework Set 3 Fall 2009
Physics 139B Solutions to Hoework Set 3 Fall 009 1. Consider a particle of ass attached to a rigid assless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 17th February 2010 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion
More informationA nonstandard cubic equation
MATH-Jan-05-0 A nonstandard cubic euation J S Markoitch PO Box West Brattleboro, VT 050 Dated: January, 05 A nonstandard cubic euation is shown to hae an unusually econoical solution, this solution incorporates
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 informationChapter 6 1-D Continuous Groups
Chapter 6 1-D Continuous Groups Continuous groups consist of group eleents labelled by one or ore continuous variables, say a 1, a 2,, a r, where each variable has a well- defined range. This chapter explores:
More informationNewton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics
Lecture 2 Key Concepts Newtonian echanics and relation to Kepler's laws The Virial Theore Tidal forces Collision physics Newton's Laws 1) An object at rest will reain at rest and an object in otion will
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 informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 9th February 011 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion of
More informationCalculations Manual 5-1
Calculations Manual 5-1 Although you ay be anxious to begin building your rocket, soe iportant decisions need to be ade about launch conditions that can help ensure a ore accurate launch. Reeber: the goal
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 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 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 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 informationModel Fitting. CURM Background Material, Fall 2014 Dr. Doreen De Leon
Model Fitting CURM Background Material, Fall 014 Dr. Doreen De Leon 1 Introduction Given a set of data points, we often want to fit a selected odel or type to the data (e.g., we suspect an exponential
More informationGeneral Physics General Physics General Physics General Physics. Language of Physics
1 Physics is a science rooted equally firly in theory and experients Physicists observe Nature series of experients easure physical quantities discover how the things easured are connected discover a physical
More information2009 Academic Challenge
009 Acadeic Challenge PHYSICS TEST - REGIONAL This Test Consists of 5 Questions Physics Test Production Tea Len Stor, Eastern Illinois University Author/Tea Leader Doug Brandt, Eastern Illinois University
More informationEgyptian Mathematics Problem Set
(Send corrections to cbruni@uwaterloo.ca) Egyptian Matheatics Proble Set (i) Use the Egyptian area of a circle A = (8d/9) 2 to copute the areas of the following circles with given diaeter. d = 2. d = 3
More informationPart A Here, the velocity is at an angle of 45 degrees to the x-axis toward the z-axis. The velocity is then given in component form as.
Electrodynaics Chapter Andrew Robertson 32.30 Here we are given a proton oving in a agnetic eld ~ B 0:5^{ T at a speed of v :0 0 7 /s in the directions given in the gures. Part A Here, the velocity is
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 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 informationDimensions and Units
Civil Engineering Hydraulics Mechanics of Fluids and Modeling Diensions and Units You already know how iportant using the correct diensions can be in the analysis of a proble in fluid echanics If you don
More informationCONNECTED RATE OF CHANGE PACK
C4 CONNECTED RATE OF CHANGE PACK 1. A vase with a circular cross-section is shown in. Water is flowing into the vase. When the depth of the water is h cm, the volume of water V cm 3 is given by V = 4 πh(h
More informationPractice Final Exam PY 205 Monday 2004 May 3
Practice Final Exa PY 05 Monday 004 May 3 Nae There are THREE forula pages. Read all probles carefully before attepting to solve the. Your work ust be legible, and the organization ust be clear. Correct
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 informationUnits conversion is often necessary in calculations
Easy Units Conversion Methodology Igathinathane Cannayen, Departent of Agricultural and Biosystes Engineering, NDSU, Fargo, ND Units conversion is often necessary in culations as any types of units were
More informationWhat is the instantaneous acceleration (2nd derivative of time) of the field? Sol. The Euler-Lagrange equations quickly yield:
PHYSICS 75: The Standard Model Midter Exa Solution Key. [3 points] Short Answer (6 points each (a In words, explain how to deterine the nuber of ediator particles are generated by a particular local gauge
More informationCompression and Predictive Distributions for Large Alphabet i.i.d and Markov models
2014 IEEE International Syposiu on Inforation Theory Copression and Predictive Distributions for Large Alphabet i.i.d and Markov odels Xiao Yang Departent of Statistics Yale University New Haven, CT, 06511
More informationPHYSICS 2210 Fall Exam 4 Review 12/02/2015
PHYSICS 10 Fall 015 Exa 4 Review 1/0/015 (yf09-049) A thin, light wire is wrapped around the ri of a unifor disk of radius R=0.80, as shown. The disk rotates without friction about a stationary horizontal
More informationLinear Transformations
Linear Transforations Hopfield Network Questions Initial Condition Recurrent Layer p S x W S x S b n(t + ) a(t + ) S x S x D a(t) S x S S x S a(0) p a(t + ) satlins (Wa(t) + b) The network output is repeatedly
More informationPart I: How Dense Is It? Fundamental Question: What is matter, and how do we identify it?
Part I: How Dense Is It? Fundaental Question: What is atter, and how do we identify it? 1. What is the definition of atter? 2. What do you think the ter ass per unit volue eans? 3. Do you think that a
More informationKernel Methods and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley ENSIAG 2 / osig 1 Second Seester 2012/2013 Lesson 20 2 ay 2013 Kernel ethods and Support Vector achines Contents Kernel Functions...2 Quadratic
More informationChemistry Department Al-kharj, October Prince Sattam Bin Abdulaziz University First semester (1437/1438)
Exercise 1 Exercises- chapter-1- Properties of gases (Part-2- Real gases Express the van der Waals paraeters a = 1.32 at d 6 ol 2 and b = 0.0436 d 3 ol 1 in SI base units? * The SI unit of pressure is
More informationSupplementary Information for Design of Bending Multi-Layer Electroactive Polymer Actuators
Suppleentary Inforation for Design of Bending Multi-Layer Electroactive Polyer Actuators Bavani Balakrisnan, Alek Nacev, and Elisabeth Sela University of Maryland, College Park, Maryland 074 1 Analytical
More informationChapter 29 Solutions
Chapter 29 Solutions 29.1 (a) up out of the page, since the charge is negative. (c) no deflection (d) into the page 29.2 At the equator, the Earth's agnetic field is horizontally north. Because an electron
More information1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along
(40) Gravitational Systes Two heavy spherical (radius 0.05) objects are located at fixed positions along 2M 2M 0 an axis in space. The first ass is centered at r = 0 and has a ass of 2M. The second ass
More informationWhat is mass? What is inertia? Turn to a partner and discuss. Turn to a new partner and discuss. Mass is. Newton s Law of Universal Gravitation
Turn to a partner and discuss Newton s Law of Universal Gravitation ass? Mass is the aount of atter in an object.! a easure of the inertia of an object.! easured in units of kilogras.! constant everywhere.!!
More informationImportant Formulae & Basic concepts. Unit 3: CHAPTER 4 - MAGNETIC EFFECTS OF CURRENT AND MAGNETISM CHAPTER 5 MAGNETISM AND MATTER
Iportant Forulae & Basic concepts Unit 3: CHAPTER 4 - MAGNETIC EFFECTS OF CURRENT AND MAGNETISM CHAPTER 5 MAGNETISM AND MATTER S. No. Forula Description 1. Magnetic field induction at a point due to current
More informationMOI (SEM. II) EXAMINATION.
Problems Based On Centroid And MOI (SEM. II) EXAMINATION. 2006-07 1- Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R. 2- State the parallel axis theorem.
More informationPhysics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10
There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference
More informationwhich is the moment of inertia mm -- the center of mass is given by: m11 r m2r 2
Chapter 6: The Rigid Rotator * Energy Levels of the Rigid Rotator - this is the odel for icrowave/rotational spectroscopy - a rotating diatoic is odeled as a rigid rotator -- we have two atos with asses
More informationField Mass Generation and Control. Chapter 6. The famous two slit experiment proved that a particle can exist as a wave and yet
111 Field Mass Generation and Control Chapter 6 The faous two slit experient proved that a particle can exist as a wave and yet still exhibit particle characteristics when the wavefunction is altered by
More informationQuestion. From Last Time. Acceleration = Velocity of the moon. How has the velocity changed? Earth s pull on the moon. Newton s three laws of motion:
Fro Last Tie Newton s three laws of otion: 1) Law of inertia ) F=a ( or a=f/ ) 3) Action and reaction (forces always coe in pairs Question If an apple falls toward the Earth, why doesn t the oon fall toward
More informationMAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START
Laboratory Section: Last Revised on Deceber 15, 2014 Partners Naes: Grade: EXPERIMENT 8 Electron Beas 0. Pre-Laboratory Work [2 pts] 1. Nae the 2 forces that are equated in order to derive the charge to
More informationSRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES
SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet
More informationModule #1: Units and Vectors Revisited. Introduction. Units Revisited EXAMPLE 1.1. A sample of iron has a mass of mg. How many kg is that?
Module #1: Units and Vectors Revisited Introduction There are probably no concepts ore iportant in physics than the two listed in the title of this odule. In your first-year physics course, I a sure that
More informationAVOIDING PITFALLS IN MEASUREMENT UNCERTAINTY ANALYSIS
VOIDING ITFLLS IN ESREENT NERTINTY NLYSIS Benny R. Sith Inchwor Solutions Santa Rosa, Suary: itfalls, both subtle and obvious, await the new or casual practitioner of easureent uncertainty analysis. This
More informationSir Isaac Newton. Newton s Laws of Motion. Mass. First Law of Motion. Weight. Weight
Sir Isaac Newton Newton s Laws of Motion Suppleental Textbook Material Pages 300-320 Born 1642 1665 began individual studies Proved universal gravitation Invented the Calculus Reflector telescope 1672
More informationIntelligent Systems: Reasoning and Recognition. Perceptrons and Support Vector Machines
Intelligent Systes: Reasoning and Recognition Jaes L. Crowley osig 1 Winter Seester 2018 Lesson 6 27 February 2018 Outline Perceptrons and Support Vector achines Notation...2 Linear odels...3 Lines, Planes
More informationTHE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE
Bulletin of the Transilvania University of Braşov Series II: Forestry Wood Industry Agricultural Food Engineering Vol. 5 (54) No. 1-1 THE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE
More informationChapter GRAVITATION. Activity Gravitation. Let us try to understand the motion of the moon by recalling activity 8.11.
Chapter 10 GRAVITATION In Chapters 8 and 9, we have learnt about the otion of objects and force as the cause of otion. We have learnt that a force is needed to change the speed or the direction of otion
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 informationWork, Energy and Momentum
Work, Energy and Moentu Work: When a body oves a distance d along straight line, while acted on by a constant force of agnitude F in the sae direction as the otion, the work done by the force is tered
More informationEffects of an Inhomogeneous Magnetic Field (E =0)
Effects of an Inhoogeneous Magnetic Field (E =0 For soe purposes the otion of the guiding centers can be taken as a good approxiation of that of the particles. ut it ust be recognized that during the particle
More informationLeast Squares Fitting of Data
Least Squares Fitting of Data David Eberly, Geoetric Tools, Redond WA 98052 https://www.geoetrictools.co/ This work is licensed under the Creative Coons Attribution 4.0 International License. To view a
More information( ') ( ) 3. Magnetostatic Field Introduction
3. Magnetostatic Field 3.. Introduction A agnetostatic field is a agnetic field produced by electric charge in peranent unifor oveent, i.e. in a peranent oveent with constant velocity. Any directed oveent
More informationChapter 6 Planar Kinetics of a Rigid Body: Force and Acceleration
Chapter 6 Planar Kinetics of a Rigid Body: Force and Acceleration Dr. Khairul Salleh Basaruddin Applied Mechanics Division School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) khsalleh@unimap.edu.my
More informationFinal Exam, vers Physics Fall, 2012
1 Final Exa, - Physics 1110 - Fall, 01 NAME Signature Student ID # TA s Nae(Circle one): Clarissa Briner, Effie Fine, Mathis Habich, Ada Keith, Willia Lewis, John Papaioannou, WeisenShen, JiayiXie, Jian
More informationEFFECTIVE MODAL MASS & MODAL PARTICIPATION FACTORS Revision I
EFFECTIVE MODA MASS & MODA PARTICIPATION FACTORS Revision I B To Irvine Eail: to@vibrationdata.co Deceber, 5 Introduction The effective odal ass provides a ethod for judging the significance of a vibration
More informationMA304 Differential Geometry
MA304 Differential Geoetry Hoework 4 solutions Spring 018 6% of the final ark 1. The paraeterised curve αt = t cosh t for t R is called the catenary. Find the curvature of αt. Solution. Fro hoework question
More informationPhysics 215 Winter The Density Matrix
Physics 215 Winter 2018 The Density Matrix The quantu space of states is a Hilbert space H. Any state vector ψ H is a pure state. Since any linear cobination of eleents of H are also an eleent of H, it
More informationKinetics of Rigid (Planar) Bodies
Kinetics of Rigi (Planar) Boies Types of otion Rectilinear translation Curvilinear translation Rotation about a fixe point eneral planar otion Kinetics of a Syste of Particles The center of ass for a syste
More informationChapter 1 Systems of Measurement
Chapter Systes of Measureent Conceptual Probles * Deterine the Concept he fundaental physical quantities in the SI syste include ass, length, and tie. Force, being the product of ass and acceleration,
More informationi ij j ( ) sin cos x y z x x x interchangeably.)
Tensor Operators Michael Fowler,2/3/12 Introduction: Cartesian Vectors and Tensors Physics is full of vectors: x, L, S and so on Classically, a (three-diensional) vector is defined by its properties under
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 informationPhysically Based Modeling CS Notes Spring 1997 Particle Collision and Contact
Physically Based Modeling CS 15-863 Notes Spring 1997 Particle Collision and Contact 1 Collisions with Springs Suppose we wanted to ipleent a particle siulator with a floor : a solid horizontal plane which
More informationPLASMA PHYSICS. 1. Charge particle motion in fields of force 2. Plasma particles and their interaction 3. Characteristic propriety of plasma
PLASMA PHYSICS 1. Charge particle otion in fields of force. Plasa particles and their interaction 3. Characteristic propriety of plasa 1 1. CHARG PARTICL MOTION IN FILDS OF FORC quations of otion: F =
More informationXII-IC (C/F) : 11/12/ (i) m As per question, pulley to be considered as a circular disc. Angular acceleration of the pulley is
CDE REVISIN NARAYANA I I T / N E E T A C A D E M Y REVISIN TEST - 0 XII-IC (C/F) : //07..... 6. 7. 8. 9. 0........ PHYSICS 6. 7. 8. 9. 0...... 6. 7. 8. 9. 0...... 6. 7. 8. 9. 0...... CHEMISTRY 6. 7. 8.
More informationCHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS
CHAPTER 21 MAGNETIC FORCES AND MAGNETIC FIELDS PROBLEMS 5. SSM REASONING According to Equation 21.1, the agnitude of the agnetic force on a oving charge is F q 0 vb sinθ. Since the agnetic field points
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 informationInfluence lines for statically indeterminate structures. I. Basic concepts about the application of method of forces.
Influence lines for statically indeterinate structures I. Basic concepts about the application of ethod of forces. The plane frae structure given in Fig. is statically indeterinate or redundant with degree
More informationAbout the definition of parameters and regimes of active two-port networks with variable loads on the basis of projective geometry
About the definition of paraeters and regies of active two-port networks with variable loads on the basis of projective geoetry PENN ALEXANDR nstitute of Electronic Engineering and Nanotechnologies "D
More information1 The properties of gases The perfect gas
1 The properties of gases 1A The perfect gas Answers to discussion questions 1A. The partial pressure of a gas in a ixture of gases is the pressure the gas would exert if it occupied alone the sae container
More informationREDUCTION OF FINITE ELEMENT MODELS BY PARAMETER IDENTIFICATION
ISSN 139 14X INFORMATION TECHNOLOGY AND CONTROL, 008, Vol.37, No.3 REDUCTION OF FINITE ELEMENT MODELS BY PARAMETER IDENTIFICATION Riantas Barauskas, Vidantas Riavičius Departent of Syste Analysis, Kaunas
More informationBlock designs and statistics
Bloc designs and statistics Notes for Math 447 May 3, 2011 The ain paraeters of a bloc design are nuber of varieties v, bloc size, nuber of blocs b. A design is built on a set of v eleents. Each eleent
More informationMECHANICS of FLUIDS INSTRUCTOR'S SOLUTIONS MANUAL TO ACCOMPANY FOURTH EDITION. MERLE C. POTTER Michigan State University DAVID C.
INSTRUCTOR'S SOLUTIONS MANUAL TO ACCOMPANY MECHANICS of FLUIDS FOURTH EDITION MERLE C. POTTER Michigan State University DAVID C. WIGGERT Michigan State University BASSEM RAMADAN Kettering University Contents
More informationPhysics 6A. Stress, Strain and Elastic Deformations. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Physics 6 Stress, Strain and Elastic Deforations When a force is applied to an object, it will defor. If it snaps back to its original shape when the force is reoved, then the deforation was ELSTIC. We
More informationStern-Gerlach Experiment
Stern-Gerlach Experient HOE: The Physics of Bruce Harvey This is the experient that is said to prove that the electron has an intrinsic agnetic oent. Hydrogen like atos are projected in a bea through a
More informationOn The Mechanics of Tone Arms
On Dick Pierce Professional Audio Developent Wherein we explore soe of the basic physical echanics of tone ars. INTRODUCTION Mechanics is a branch of physics that explores the behavior and analysis of
More information8.1 Force Laws Hooke s Law
8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which
More information16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 30: Dynamics of Turbopump Systems: The Shuttle Engine
6.5, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 30: Dynaics of Turbopup Systes: The Shuttle Engine Dynaics of the Space Shuttle Main Engine Oxidizer Pressurization Subsystes Selected Sub-Model
More informationChapter 11: Vibration Isolation of the Source [Part I]
Chapter : Vibration Isolation of the Source [Part I] Eaple 3.4 Consider the achine arrangeent illustrated in figure 3.. An electric otor is elastically ounted, by way of identical isolators, to a - thick
More information