Angular momentum Vector product.
|
|
- Laureen Lindsay Lambert
- 5 years ago
- Views:
Transcription
1 Lecture 19 Chapter 11 Physics I Angular momentum Vector product. Course website: Lecture Capture:
2 Outline Chapter 11 Angular Momentum Vector Cross Product Conservation of Ang. Mom. Ang. Mom. of point particle Rigid Objects
3 Let s introduce Vector Cross Product
4 If we have two vectors Then the vector product is Vector Cross Product B A C A B Magnitude C A B ABsin Direction: perp. to both A and B (right hand rule) Order matters: C A B B A A B
5 θ=0 A A B 0 B The vector product is zero when vectors are parallel Cross product C A B ABsin A 1 B 2 AB B A 1 B 2 θ=30 A AB The vector product increases C A B A B B AB θ=90 A A B AB The vector product is max when vectors are perpendicular The cross product vector increases from 0 to AB as θ increases from 0 to 90
6 ConcepTest 1 Vector product iˆ, ˆ, j kˆ For the unit vectors Find the following vector products 1) iˆ iˆ? 2) iˆ ˆj? C A B ABsin A) B) C) 1) iˆ iˆ 2) iˆ ˆj 1) iˆ iˆ 2) iˆ ˆj 1) iˆ iˆ 2) iˆ ˆj y iˆ 0 0 kˆ 0 ˆj iˆ iˆ iˆ ˆj 0 kˆ z x
7 A A x î A y ĵ A z ˆk Vector Cross Product ˆ ˆ ˆ ˆ i i i i Sin0 0 ˆ ˆ ˆ ˆ i j i j Sin90 1 î î 0 ĵ ĵ 0 ˆk ˆk 0 î ĵ ˆk ĵ ˆk î ˆk î ĵ B B x î B y ĵ B z ˆk A B (A x î A y ĵ A z ˆk) (Bx î B y ĵ B z ˆk) A x B x (î î ) A B (î ĵ) A B x y x z (î ˆk) A y B x ( ĵ î ) A yb y ( ĵ ĵ) A yb z ( ĵ ˆk) A z B x ( ˆk î ) A zb y ( ˆk ĵ) A zb z ( ˆk ˆk) (A y B z A z B y )î (A zb x A x B z ) ĵ (A xb y A y B x ) ˆk
8 Vector Cross Product. Example What is the vector cross product of the two vectors: A 1î 2 ĵ 4 ˆk B 2î 3ĵ 1ˆk A B (A y B z A z B y )î (A zb x A x B z ) ĵ (A xb y A y B x ) ˆk A B [(2 1) (4 3)]î [(4 2) (11)] ĵ [(13) (2 2)]ˆk A B 14î 9 ĵ 1 ˆk
9 Write Torque as the Cross Product F Let s look at a door top view: Axis of rotation r Applied force F produces torque rf sin Now, with vector product notation we can rewrite torque as r F Torque direction out of page (right hand rule) Notation convention: Direction out of the page Direction into the page
10 Angular Momentum
11 For translational motion we needed the concepts of force, F linear momentum, p mass, m For rotational motion we needed the concepts of torque, angular momentum, L moment of inertia, I Angular momentum is the rotational equivalent of linear momentum p mv L?
12 y Angular Momentum of a single particle z L r p x p O r r m p L r p Suppose we have a particle with -linear momentum -positioned at r O Then, by definition: Angular momentum of a particle about point O is L rpsin Carefull: Let s calculate angular momentum of m about point O L r p since r p, rpsin 0 so 0, sin 0 Thus, angular momentum of m O 0 L but L 0 O Cont.
13 Angular Momentum is not an intrinsic property of a particle. It depends on a choice of origin So, never forget to indicate which origin is being used
14 By definition: L r p Example: projectile motion What is the angular momentum of a free particle of mass m moving near the surface of the Earth? y p 0 A O r p x Let s calculate the angular momentum of a particle about point O. 1) L at point O: L L r p 0 sin 0 L L r psin 0 2) L at point A: 0 So, the angular momentum is changing.
15 Example: the Earth around the Sun. What is the angular momentum of a particle of mass m moving with speed v=const in a circle of radius r in a counterclockwise direction? By definition: L r p L r p Let s calculate the angular momentum of a particle about point O. m p L θ=90 L L rpsin rmv So, the angular momentum is constant. The magnitude is O r const The direction of the angular momentum is perpendicular to the plane of circle (right-hand rule) But, again, L calculated relative to O is obviously not a constant. It depends on a choice of origin
16 Angular Momentum of a rigid body For the rotation of a symmetrical object about the symmetry axis, the angular momentum and the angular velocity are related by (without a proof) L I L I I moment of inertia of a body L points towards L I L I
17 Two definitions of Angular Momentum Single particle L r p L r p Rigid symmetrical body L I L
18 dl dl Rotational N. 2 nd law Let s find relationship between angular momentum and torque for a point particle: dr L r p p 0 mv r F v dl r dp N. 2 nd law F p mv Rotational N. 2nd law written in terms of L. Torque causes the particle s angular momentum to change dp
19 Rotational N. 2 nd law Let s show that this rotational N. 2 nd law is the same to the one presented in Lecture 18 I I d I We got exactly the same expression d ( I ) dl dl Translational N.2 nd law F F ma dp Rotational N.2 nd law I dl
20 Example:What is the angular momentum (about the origin) of an object of mass m dropped from rest.
21 ConcepTest 2 traffic light/car A car of mass 1000 kg drives away from a traffic light h=10 m high, as shown below, at a constant speed of v=10 m/s. What is the angular momentum of the car with respect to the light? A) B) C) 100,000( kˆ) 10,000( kˆ) 100,000 iˆ kgm kgm kgm s s s z x h y r v L r p mv( rsin )( kˆ) mvh( kˆ ) 100,000( k ˆ )
22 Conservation of Angular Momentum Angular momentum is an important concept because, under certain conditions, it is conserved. dl If the net external torque on an object is zero, then the total angular momentum is conserved. If net net dl 0, then L const 0 L I L 1 L For a rigid body 2 I 1 1 I 2 2
23 Thank you See you on Monday
Angular momentum Vector product.
Lecture 19 Chapter 11 Physics I 11.20.2013 Angular momentum Vector product. Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationLecture 20 Chapter 12 Angular Momentum Course website:
Lecture 20 Chapter 12 Angular Momentum Another Law? Am I in a Law school? Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational
More informationAngular Momentum Conservation of Angular Momentum
Lecture 22 Chapter 12 Physics I Angular Momentum Conservation of Angular Momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational
More informationCross Product Angular Momentum
Lecture 21 Chapter 12 Physics I Cross Product Angular Momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics
More informationWork and Energy (Work Done by a Constant Force)
Lecture 11 Chapter 7 Physics I 10.16.2013 Work and Energy (Work Done by a Constant Force) Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationConservation of Angular momentum
ecture 20 Chapter 11 Physics I 04.14.2014 Conservation of Angular momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi ecture Capture: http://echo360.uml.edu/danylov2013/physics1spring.html
More informationModule 24: Angular Momentum of a Point Particle
24.1 Introduction Module 24: Angular Momentum of a Point Particle When we consider a system of objects, we have shown that the external force, acting at the center of mass of the system, is equal to the
More informationPhysics 101 Lecture 11 Torque
Physics 101 Lecture 11 Torque Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Force vs. Torque q Forces cause accelerations q What cause angular accelerations? q A door is free to rotate about an axis
More informationConservation of Angular Momentum
Lecture 23 Chapter 12 Physics I Conservation of Angular Momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics
More informationGeneral Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10
Units of Chapter 10 Determining Moments of Inertia Rotational Kinetic Energy Rotational Plus Translational Motion; Rolling Why Does a Rolling Sphere Slow Down? General Definition of Torque, final Taking
More informationStatic Equilibrium. Lecture 21. Chapter 12. Physics I Department of Physics and Applied Physics
Lecture 21 Chapter 12 Physics I 11.27.2013 Static Equilibrium Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationRotational N.2 nd Law
Lecture 19 Chapter 12 Rotational N.2 nd Law Torque Newton 2 nd Law again!? That s it. He crossed the line! Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will
More informationPhys101 First Major-111 Zero Version Monday, October 17, 2011 Page: 1
Monday, October 17, 011 Page: 1 Q1. 1 b The speed-time relation of a moving particle is given by: v = at +, where v is the speed, t t + c is the time and a, b, c are constants. The dimensional formulae
More informationRotational Motion. Lecture 17. Chapter 10. Physics I Department of Physics and Applied Physics
Lecture 17 Chapter 10 Physics I 11.13.2013 otational Motion Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationChapter 11. Angular Momentum
Chapter 11 Angular Momentum Angular Momentum Angular momentum plays a key role in rotational dynamics. There is a principle of conservation of angular momentum. In analogy to the principle of conservation
More informationPhysics 121, March 27, Angular Momentum, Torque, and Precession. Department of Physics and Astronomy, University of Rochester
Physics 121, March 27, 2008. Angular Momentum, Torque, and Precession. Physics 121. March 27, 2008. Course Information Quiz Topics to be discussed today: Review of Angular Momentum Conservation of Angular
More informationRotational N.2 nd Law
Lecture 0 Chapter 1 Physics I Rotational N. nd Law Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics Today
More informationAngular Momentum. Objectives CONSERVATION OF ANGULAR MOMENTUM
Angular Momentum CONSERVATION OF ANGULAR MOMENTUM Objectives Calculate the angular momentum vector for a moving particle Calculate the angular momentum vector for a rotating rigid object where angular
More informationAngular Momentum. Physics 1425 Lecture 21. Michael Fowler, UVa
Angular Momentum Physics 1425 Lecture 21 Michael Fowler, UVa A New Look for τ = Iα We ve seen how τ = Iα works for a body rotating about a fixed axis. τ = Iα is not true in general if the axis of rotation
More informationLecture-XII. Angular momentum and Fixed axis rotation
Lecture-XII Angular momentum and Fixed axis rotation Angular Momentum of a System of Particles Consider a collection of N discrete particles. The total angular momentum of the system is The force acting
More informationRotational Motion. Lecture 17. Chapter 10. Physics I Department of Physics and Applied Physics
Lecture 17 Chapter 10 Physics I 04.0.014 otational Motion Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov013/physics1spring.html
More informationChapter 6: Vector Analysis
Chapter 6: Vector Analysis We use derivatives and various products of vectors in all areas of physics. For example, Newton s 2nd law is F = m d2 r. In electricity dt 2 and magnetism, we need surface and
More informationPhysics 218 Lecture 21
Physics 218 Lecture 21 Dr. David Toback Physics 218, Lecture XXI 1 Checklist for Today Things due Yesterday Chapters 12 & 13 in WebCT Things that are due for today Read Chapters 14-16 Things that are due
More informationChapters 10 & 11: Rotational Dynamics Thursday March 8 th
Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Review of rotational kinematics equations Review and more on rotational inertia Rolling motion as rotation and translation Rotational kinetic energy
More informationChapter 19 Angular Momentum
Chapter 19 Angular Momentum Chapter 19 Angular Momentum... 2 19.1 Introduction... 2 19.2 Angular Momentum about a Point for a Particle... 3 19.2.1 Angular Momentum for a Point Particle... 3 19.2.2 Right-Hand-Rule
More informationPhysics UCSB TR 2:00-3:15 lecture Final Exam Wednesday 3/17/2010
Physics @ UCSB TR :00-3:5 lecture Final Eam Wednesday 3/7/00 Print your last name: Print your first name: Print your perm no.: INSTRUCTIONS: DO NOT START THE EXAM until you are given instructions to do
More informationis acting on a body of mass m = 3.0 kg and changes its velocity from an initial
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
More informationThe Vector Product. ! a. !! a! b = c. a.k.a. The Cross Product. ! c. c =! a! b sin! multiply two vectors... get a vector. magnitude: direction:
Angular Momentum a b The Vector Product a.k.a. The Cross Product a b = c multiply two vectors... get a vector c = a b sin magnitude: direction: c and lie in a plane.* Their cross product is a vector perpendicular
More informationLecture Outline Chapter 11. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 11 Physics, 4 th Edition James S. Walker Chapter 11 Rotational Dynamics and Static Equilibrium Units of Chapter 11 Torque Torque and Angular Acceleration Zero Torque and Static
More informationIntroduction to vectors
Lecture 4 Introduction to vectors Course website: http://facult.uml.edu/andri_danlov/teaching/phsicsi Lecture Capture: http://echo360.uml.edu/danlov2013/phsics1fall.html 95.141, Fall 2013, Lecture 3 Outline
More informationPhysics 1A Lecture 10B
Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to
More informationLesson 8. Luis Anchordoqui. Physics 168. Thursday, October 11, 18
Lesson 8 Physics 168 1 Rolling 2 Intuitive Question Why is it that when a body is rolling on a plane without slipping the point of contact with the plane does not move? A simple answer to this question
More informationChapter 1. Units, Physical Quantities, and Vectors
Chapter 1 Units, Physical Quantities, and Vectors 1.3 Standards and Units The metric system is also known as the S I system of units. (S I! Syst me International). A. Length The unit of length in the metric
More informationare (0 cm, 10 cm), (10 cm, 10 cm), and (10 cm, 0 cm), respectively. Solve: The coordinates of the center of mass are = = = (200 g g g)
Rotational Motion Problems Solutions.. Model: A spinning skater, whose arms are outstretched, is a rigid rotating body. Solve: The speed v rω, where r 40 / 0.70 m. Also, 80 rpm (80) π/60 rad/s 6 π rad/s.
More informationWork and Kinetic Energy
Lecture 12 Chapter 9 Work and Kinetic Energy I am sick and tired of your forces!!! Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will learn how to solve problems
More informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 12: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational 2 / / 1/ 2 m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv 2 /
More informationProblem Solving Session 11 Three Dimensional Rotation and Gyroscopes Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Problem Solving Session 11 Three Dimensional Rotation and Gyroscopes Solutions W14D3-1 Rotating Skew Rod Solution Consider a simple
More informationPhys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw
Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the
More informationLectures. Today: Rolling and Angular Momentum in ch 12. Complete angular momentum (chapter 12) and begin equilibrium (chapter 13)
Lectures Today: Rolling and Angular Momentum in ch 1 Homework 6 due Next time: Complete angular momentum (chapter 1) and begin equilibrium (chapter 13) By Monday, will post at website Sample midterm II
More informationChapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More informationChapter 11 Rolling, Torque, and Angular Momentum
Prof. Dr. I. Nasser Chapter11-I November, 017 Chapter 11 Rolling, Torque, and Angular Momentum 11-1 ROLLING AS TRANSLATION AND ROTATION COMBINED Translation vs. Rotation General Rolling Motion General
More informationChapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis
Chapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis Chapter 21 Rigid Body Dynamics: Rotation and Translation about a Fixed Axis... 2 21.1 Introduction... 2 21.2 Translational Equation
More informationHandout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a
More informationPHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011
PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this
More informationSpring Force and Power
Lecture 14 Chapter 9 Physics I Spring Force and Power Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will learn how to solve problems using two new concepts:
More information2.003 Engineering Dynamics Problem Set 4 (Solutions)
.003 Engineering Dynamics Problem Set 4 (Solutions) Problem 1: 1. Determine the velocity of point A on the outer rim of the spool at the instant shown when the cable is pulled to the right with a velocity
More informationChapter 11. Angular Momentum
Chapter 11 Angular Momentum Angular Momentum Angular momentum plays a key role in rotational dynamics. There is a principle of conservation of angular momentum. In analogy to the principle of conservation
More informationProf. Rupak Mahapatra. Physics 218, Chapter 15 & 16
Physics 218 Chap 14 & 15 Prof. Rupak Mahapatra Physics 218, Chapter 15 & 16 1 Angular Quantities Position Angle θ Velocity Angular Velocity ω Acceleration Angular Acceleration α Moving forward: Force Mass
More informationGeneral Physics I. Lecture 8: Rotation of a Rigid Object About a Fixed Axis. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 8: Rotation of a Rigid Object About a Fixed Axis Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ New Territory Object In the past, point particle (no rotation,
More informationRolling, Torque & Angular Momentum
PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the
More informationPhysics 121, March 25, Rotational Motion and Angular Momentum. Department of Physics and Astronomy, University of Rochester
Physics 121, March 25, 2008. Rotational Motion and Angular Momentum. Physics 121. March 25, 2008. Course Information Topics to be discussed today: Review of Rotational Motion Rolling Motion Angular Momentum
More informationKing Fahd University of Petroleum and Minerals Physics Department Physics 101 Recitation Term 131 Fall 013 Quiz # 4 Section 10 A 1.50-kg block slides down a frictionless 30.0 incline, starting from rest.
More informationPhysics 1 Second Midterm Exam (AM) 2/25/2010
Physics Second Midterm Eam (AM) /5/00. (This problem is worth 40 points.) A roller coaster car of m travels around a vertical loop of radius R. There is no friction and no air resistance. At the top of
More informationMath Review Night: Work and the Dot Product
Math Review Night: Work and the Dot Product Dot Product A scalar quantity Magnitude: A B = A B cosθ The dot product can be positive, zero, or negative Two types of projections: the dot product is the parallel
More informationFigure 17.1 The center of mass of a thrown rigid rod follows a parabolic trajectory while the rod rotates about the center of mass.
17.1 Introduction A body is called a rigid body if the distance between any two points in the body does not change in time. Rigid bodies, unlike point masses, can have forces applied at different points
More information8 Rotational motion of solid objects
8 Rotational motion of solid objects Kinematics of rotations PHY166 Fall 005 In this Lecture we call solid objects such extended objects that are rigid (nondeformable) and thus retain their shape. In contrast
More informationA B Ax Bx Ay By Az Bz
Lecture 5.1 Dynamics of Rotation For some time now we have been discussing the laws of classical dynamics. However, for the most part, we only talked about examples of translational motion. On the other
More informationLecture 3- Vectors Chapter 3
1 / 36 Lecture 3- Vectors Chapter 3 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 21 th, 2018 2 / 36 Course Reminders The course
More informationIntroduction to Vector Calculus (29) SOLVED EXAMPLES. (d) B. C A. (f) a unit vector perpendicular to both B. = ˆ 2k = = 8 = = 8
Introduction to Vector Calculus (9) SOLVED EXAMPLES Q. If vector A i ˆ ˆj k, ˆ B i ˆ ˆj, C i ˆ 3j ˆ kˆ (a) A B (e) A B C (g) Solution: (b) A B (c) A. B C (d) B. C A then find (f) a unit vector perpendicular
More informationConservation of Energy
Lecture 3 Chapter 8 Physics I 03.0.04 Conservation of Energy Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov03/physicsspring.html
More informationQ: What does angular momentum mean? What is its equation for calculation?
Ch 10: Conservation of Angular Momentum Reeeeecap. Q: What does angular velocity mean? What is its symbol? A: The rate of change of angular displacement.. Q: What does angular acceleration mean? What is
More informationRotation Angular Momentum
Rotation Angular Momentum Lana Sheridan De Anza College Nov 28, 2017 Last time rolling motion Overview Definition of angular momentum relation to Newton s 2nd law angular impulse angular momentum of rigid
More informationStatic Equilibrium. Lecture 24. Chapter 12. Physics I. Department of Physics and Applied Physics
Lecture 24 Chapter 12 Physics I Static Equilibrium Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will discuss static equilibrium of an object Today we are
More informationLecture 3- Vectors Chapter 3
1 / 36 Lecture 3- Vectors Chapter 3 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 21 th, 2018 2 / 36 Course Reminders The course
More informationPhysics 131: Lecture 22. Today s Agenda
Physics 131: Lecture Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 An Unfair Race A frictionless block and a rolling (without slipping) disk are released at
More informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I
More informationModule 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis
Module 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis 27.1 Introduction We shall analyze the motion o systems o particles and rigid bodies that are undergoing translational and rotational
More informationPhysics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1
Physics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1 Physics 141. Lecture 18. Course Information. Topics to be discussed today: A
More informationGeneral Physics I. Lecture 8: Rotation of a Rigid Object About a Fixed Axis. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 8: Rotation of a Rigid Object About a Fixed Axis Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ New Territory Object In the past, point particle (no rotation,
More informationProblem 1 Problem 2 Problem 3 Problem 4 Total
Name Section THE PENNSYLVANIA STATE UNIVERSITY Department of Engineering Science and Mechanics Engineering Mechanics 12 Final Exam May 5, 2003 8:00 9:50 am (110 minutes) Problem 1 Problem 2 Problem 3 Problem
More informationPhys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1
Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2 O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see
More informationA) 1 gm 2 /s. B) 3 gm 2 /s. C) 6 gm 2 /s. D) 9 gm 2 /s. E) 10 gm 2 /s. A) 0.1 kg. B) 1 kg. C) 2 kg. D) 5 kg. E) 10 kg A) 2:5 B) 4:5 C) 1:1 D) 5:4
1. A 4 kg object moves in a circle of radius 8 m at a constant speed of 2 m/s. What is the angular momentum of the object with respect to an axis perpendicular to the circle and through its center? A)
More informationVECTORS. Vectors OPTIONAL - I Vectors and three dimensional Geometry
Vectors OPTIONAL - I 32 VECTORS In day to day life situations, we deal with physical quantities such as distance, speed, temperature, volume etc. These quantities are sufficient to describe change of position,
More informationPY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I
PY205N Spring 2013 Final exam, practice version MODIFIED This practice exam is to help students prepare for the final exam to be given at the end of the semester. Please note that while problems on this
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More informationPhysics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium
Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More informationWork and kinetic Energy
Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg
More informationSOLUTIONS TO CONCEPTS CHAPTER 2
SOLUTIONS TO CONCPTS CHAPTR 1. As shown in the figure, The angle between A and B = 11 = 9 A = and B = 4m Resultant R = A B ABcos = 5 m Let be the angle between R and A 4 sin9 = tan 1 = tan 1 (4/) = 5 4cos9
More informationCircular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics
Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av
More informationPhys 270 Final Exam. Figure 1: Question 1
Phys 270 Final Exam Time limit: 120 minutes Each question worths 10 points. Constants: g = 9.8m/s 2, G = 6.67 10 11 Nm 2 kg 2. 1. (a) Figure 1 shows an object with moment of inertia I and mass m oscillating
More informationProf. Rupak Mahapatra. Dynamics of Rotational Motion
Physics 218 Chapter 12-1616 Prof. Rupak Mahapatra Dynamics of Rotational Motion 1 Overview Chapters 12-16 are about Rotational Motion While we ll do Exam 3 on Chapters 10-13, we ll do the lectures on 12-16
More informationGeneral Physics I. Lecture 9: Vector Cross Product. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 9: Vector Cross Product Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Examples of the rotation of a rigid object about a fixed axis Force/torque
More informationForces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll)
Physics 2101 Section 3 March 12 rd : Ch. 10 Announcements: Mid-grades posted in PAW Quiz today I will be at the March APS meeting the week of 15-19 th. Prof. Rich Kurtz will help me. Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101-3/
More informationPHYS 172: Modern Mechanics. Summer Lecture 2 Velocity and Momentum Read:
PHYS 172: Modern Mechanics Summer 2010 p sys F net t E W Q sys surr surr L sys net t Lecture 2 Velocity and Momentum Read: 1.6-1.9 Math Experience A) Currently taking Calculus B) Currently taking Calculus
More informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1
Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid
More informationPhysics A - PHY 2048C
Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
More information10. The dimensional formula for c) 6% d) 7%
UNIT. One of the combinations from the fundamental phsical constants is hc G. The unit of this epression is a) kg b) m 3 c) s - d) m. If the error in the measurement of radius is %, then the error in the
More informationChap11. Angular Momentum
Chap11. Angular Momentum Level : AP Physics Teacher : Kim 11.1 The Vector Product and Torque (p.335) Properties of the Vector Product For scalar product, we are familiar with +,. Ex) 3+2=5. Numbers are
More informationDEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B-1A: ROTATIONAL DYNAMICS Essential Idea: The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual
More informationPhysics 4A Solutions to Chapter 11 Homework
Physics 4A Solutions to Chapter 11 Homework Chapter 11 Questions:, 8, 10 Exercises & Problems: 1, 14, 4, 7, 37, 53, 66, 81, 83 Answers to Questions: Q 11- (a) 5 and 6 (b) 1 and 4 tie, then the rest tie
More informationPhys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1
Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see Figure
More informationparticle p = m v F ext = d P = M d v cm dt
Lecture 11: Momentum and Collisions; Introduction to Rotation 1 REVIEW: (Chapter 8) LINEAR MOMENTUM and COLLISIONS The first new physical quantity introduced in Chapter 8 is Linear Momentum Linear Momentum
More informationUNIVERSITY OF MANITOBA. All questions are of equal value. Answer all questions. No marks are subtracted for wrong answers.
PAGE NO.: 1 of 5 All questions are of equal value. Answer all questions. No marks are subtracted for wrong answers. Record all answers on the computer score sheet provided. USE PENCIL ONLY! Black pen will
More informationVectors for Physics. AP Physics C
Vectors for Physics AP Physics C A Vector is a quantity that has a magnitude (size) AND a direction. can be in one-dimension, two-dimensions, or even three-dimensions can be represented using a magnitude
More informationPHY1004W 2014 Modern Mechanics Part 4
PHY1004W 014 Modern Mechanics Part 4 Prof Andy Buffler Room 503 RW James andy.buffler@uct.ac.za These slides have benefited from significant guidance from the notes of Roger Fearick (UCT Physics) and the
More informationReview of Engineering Dynamics
Review of Engineering Dynamics Part 1: Kinematics of Particles and Rigid Bodies by James Doane, PhD, PE Contents 1.0 Course Overview... 4.0 Basic Introductory Concepts... 4.1 Introduction... 4.1.1 Vectors
More informationChapter 27 Sources of Magnetic Field
Chapter 27 Sources of Magnetic Field In this chapter we investigate the sources of magnetic of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents). Ampere s Law
More informationTwo-Dimensional Rotational Dynamics
Two-Dimensional Rotational Dynamics 8.01 W09D2 W09D2 Reading Assignment: MIT 8.01 Course Notes: Chapter 17 Two Dimensional Rotational Dynamics Sections 17.1-17.5 Chapter 18 Static Equilibrium Sections
More informationA) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2.
Coordinator: Dr. W. Al-Basheer Thursday, July 30, 2015 Page: 1 Q1. A constant force F ( 7.0ˆ i 2.0 ˆj ) N acts on a 2.0 kg block, initially at rest, on a frictionless horizontal surface. If the force causes
More information