Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics


 Lee Rice
 2 years ago
 Views:
Transcription
1 Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics
2 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 = ω t = a t t Angular Acceleration T = 2π ω = 1 f Period of Rotation
3 Formulas: Angular Kinematics Linear Equation (a = constant) v = v 0 + at x = x 0 + v 0 t at2 Angular Equation (α = constant) ω = ω 0 + αt θ = θ 0 + ω 0 t αt2 v 2 = v a(x x 0 ) ω 2 = ω α(θ θ 0 ) Tangential Quantities: v t = rω a t = rα Centripetal Acceleration: a c = v t 2 r = rω2
4 Rolling Motion (no slipping) A perfectly round object that is rolling over a surface is experiencing static friction The part of the object in contact with the surface is always at rest The linear speed v of the axle (center of the wheel) is therefore completely dependent on the angular velocity ω and the radius r of the wheel. Rolling Velocity (w/o slipping) v = rω
5 68.0 cm Example: Rolling Motion A bicycle slows down uniformly from a speed of v 0 = 8.40 m/s to rest, over a distance of 115 m. Each wheel and tire has an overall diameter of 68.0 cm. Find: a) The initial angular velocity of the wheels b) The total number of revolutions made by each wheel before coming to rest c) The angular acceleration of the wheels d) The time it took to come to a stop v 0 = 8.40 m/s v = m
6 Angular Dynamics: Torque & Moment Causing rotation obviously requires a force (Newton s 1 st Law) The direction and location of this force are highly important In the example below, a lever extends a certain length from the fulcrum (center of rotation). Several forces act on the lever. Assuming all three forces have the same magnitude, which force will cause the fastest rotation? Which force will not cause any rotation? fulcrum F C no rotation F A F B fastest rotation
7 Angular Dynamics: Torque & Moment F B will cause a greater angular acceleration for two very important reasons: Its direction is perpendicular to the lever It s applied farther from the axis of rotation (fulcrum) F C will not cause any rotation, even though it is applied farther from the fulcrum than F B This is because its direction is parallel to the lever In order to cause rotation, some component of the force must be perpendicular to the lever fulcrum F C no rotation F A F B fastest rotation
8 Angular Dynamics: Torque & Moment We can now define torque τ as the product of the perpendicular force acting on a lever and the distance away from the fulcrum this force is applied (called the lever arm) Unit: m N (meters times Newtons not the same thing as a joule, which is a N m) The greater the torque caused by a force, the greater the resulting angular acceleration (direct proportion) If the force is applied at an angle θ, we simply find the perpendicular component of that force and use it to calculate torque r ( lever arm ) F sin θ F cos θ Torque τ = rf θ F τ = rf sin θ
9 Example: Torque & Moment Two circular disks of radii r A = 30 cm and r B = 50 cm are attached to each other on an axle that passes through the center of each. Calculate the net torque on this compound disk due to the two forces shown. F A = 50 N r B r A F B = 50 N
10 Angular Dynamics: Rotational Inertia To see how torque relates to acceleration, let s examine a simple example of a particle of mass m rotating in a circle of radius r. A force F is applied to the mass in a direction tangent to the circle. The applied force will cause tangential acceleration. So we can combine the equation for tangential acceleration with the equation for Newton s Second Law: F = ma F = mrα Now, multiplying both sides by r: Torque (τ) rf = mr 2 α Moment of Inertia (I) r Torque & Moment of Inertia τ = Iα F m
11 Angular Dynamics: Rotational Inertia The moment of inertia (I) is simple for a single particle in circular motion. But a rotating rigid object (like a wheel) consists of many particles, all at different distances from the center of rotation. Therefore, the moment of inertia for a rigid object depends on the shape and density of the object and the location of the axis of rotation. The total torque on an object is related to the total moment of inertia in the following way: τ = ( mr 2 )α τ = Iα
12 Angular Dynamics: Rotational Inertia These values were computed using integral calculus; a similar table can be found in your book (Pg. 291, Table 101)
13 Example: Rotational Inertia Three forces are applied, as shown, to a solid circular disk of mass 3.50 kg and a radius of 25.0 cm (with an axis of rotation through the center) that is at rest. Calculate: a) The net torque acting on the disk b) The moment of inertia of the disk c) The resulting angular acceleration α F B = 55.0 N 30 F A = 60.0 N 25.0 cm 45 F B = 40.0 N
14 Rotational Kinetic Energy Any rigid, rotating object will have rotational kinetic energy (units are still joules): K R = 1 2 Iω2 Rotational Kinetic Energy If the object also undergoes translational motion as it spins (think: a tire rolling down a ramp or ball rolling across a floor), then it will have both rotational and translational kinetic energies: K total = K + K R = 1 2 mv Iω2 Total Kinetic Energy
15 Rotational Kinetic Energy Just like the work done by a force can be thought of as the change in kinetic energy, we can also define the work done by torque as the change in rotational kinetic energy: W = τ θ = 1 2 I ω2 Work Done by Torque This way, the work done by torque can be thought of as the work required to get an object spinning at a rate of ω, starting from rest.
16 Example: Rotational Kinetic Energy A spherical ball of mass M and radius R and a circular ring of the exact same mass and radius both sit at rest at the top of an incline at a vertical height of H. When they are released, which will reach the bottom of the incline first?
17 Angular Momentum When an object rotates or spins with angular speed ω, we say that it has angular momentum (L), and we calculate it exactly as expected: by replacing m and v with their angular analogues I and ω: L = Iω Angular Momentum Just as with other angular vector quantities, angular momentum can be translated into a tangential quantity that depends on the distance r from the center: L = rp Angular and Linear Momentum
18 Conservation of Angular Momentum World Record Figure Skating Spin: Angular momentum (just like linear momentum) will always be conserved. If net external torque is zero, it follows that final angular momentum will equal the initial angular momentum: L 1 = L 2 I 1 ω 1 = I 2 ω 2 Conservation of Angular Momentum
19 Exit Ticket: Rotational Dynamics A small mass (m = 1.5 kg) attached to the end of a string revolves in a circle on a frictionless tabletop. The other end of the string passes through a hole in the table. Initially, the mass revolves with a tangential speed of v 1 = 2.4 m/s in a circle of radius r 1 = 0.80 m. The string is then pulled so that the radius is reduced to r 2 = 0.48 m. Find: a) The final speed v 2 of the mass b) The initial and final angular speeds ω 1 and ω 2 c) The total kinetic energy before and after the radius changes Homework Problem Set: Rotational Dynamics Pg #44 60 (mult of 4) Pg #4 32 AND #4060 (mult of 4)
General 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 informationSlide 1 / 37. Rotational Motion
Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.
More informationRotational Motion and Torque
Rotational Motion and Torque Introduction to Angular Quantities Sections 8 to 82 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is
More informationChapter 8 Lecture Notes
Chapter 8 Lecture Notes Physics 2414  Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ
More informationUnit 8 Notetaking Guide Torque and Rotational Motion
Unit 8 Notetaking Guide Torque and Rotational Motion Rotational Motion Until now, we have been concerned mainly with translational motion. We discussed the kinematics and dynamics of translational motion
More informationWe define angular displacement, θ, and angular velocity, ω. What's a radian?
We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise
More information31 ROTATIONAL KINEMATICS
31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have
More informationChapter 910 Test Review
Chapter 910 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
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 informationChapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium
More informationTest 7 wersja angielska
Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationTorque and Rotation Lecture 7
Torque and Rotation Lecture 7 ˆ In this lecture we finally move beyond a simple particle in our mechanical analysis of motion. ˆ Now we consider the socalled rigid body. Essentially, a particle with extension
More information= o + t = ot + ½ t 2 = o + 2
Chapters 89 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More informationChapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc.
Chapter 10 Rotational Kinematics and Energy 101 Angular Position, Velocity, and Acceleration 101 Angular Position, Velocity, and Acceleration Degrees and revolutions: 101 Angular Position, Velocity,
More informationPhys 106 Practice Problems Common Quiz 1 Spring 2003
Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed
More information1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
AP Physics B Practice Questions: Rotational Motion MultipleChoice Questions 1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
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 informationUniform Circular Motion
Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,
More informationBig Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular
Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only
More informationChapter 8 Rotational Kinematics Angular Variables Kinematic Equations
Chapter 8 Rotational Kinematics Angular Variables Kinematic Equations Chapter 9 Rotational Dynamics Torque Center of Gravity Newton s 2 nd Law Angular Rotational Work & Energy Angular Momentum Angular
More informationUse the following to answer question 1:
Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to
More informationRotational Dynamics, Moment of Inertia and Angular Momentum
Rotational Dynamics, Moment of Inertia and Angular Momentum Now that we have examined rotational kinematics and torque we will look at applying the concepts of angular motion to Newton s first and second
More informationTranslational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
More informationChapter 8. Rotational Motion
Chapter 8 Rotational Motion Rotational Work and Energy W = Fs = s = rθ Frθ Consider the work done in rotating a wheel with a tangential force, F, by an angle θ. τ = Fr W =τθ Rotational Work and Energy
More informationLecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is
More informationAngular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion
Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for
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 informationTextbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8
AP Physics Rotational Motion Introduction: Which moves with greater speed on a merrygoround  a horse near the center or one near the outside? Your answer probably depends on whether you are considering
More informationChap10. Rotation of a Rigid Object about a Fixed Axis
Chap10. Rotation of a Rigid Object about a Fixed Axis Level : AP Physics Teacher : Kim 10.1 Angular Displacement, Velocity, and Acceleration  A rigid object rotating about a fixed axis through O perpendicular
More informationCIRCULAR MOTION AND ROTATION
1. UNIFORM CIRCULAR MOTION So far we have learned a great deal about linear motion. This section addresses rotational motion. The simplest kind of rotational motion is an object moving in a perfect circle
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 informationChapter 10. Rotation
Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGrawPHY 45 Chap_10HaRotationRevised
More informationRotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
More informationTorque. Introduction. Torque. PHY torque  J. Hedberg
Torque PHY 207  torque  J. Hedberg  2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem
More informationChapter 10. Rotation of a Rigid Object about a Fixed Axis
Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merrygoround rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular
More informationRolling, Torque, and Angular Momentum
AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where
More informationAngular Displacement. θ i. 1rev = 360 = 2π rads. = "angular displacement" Δθ = θ f. π = circumference. diameter
Rotational Motion Angular Displacement π = circumference diameter π = circumference 2 radius circumference = 2πr Arc length s = rθ, (where θ in radians) θ 1rev = 360 = 2π rads Δθ = θ f θ i = "angular displacement"
More informationWebreview Torque and Rotation Practice Test
Please do not write on test. ID A Webreview  8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30mradius automobile
More informationAP Physics 1 Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law F = Ma cm. Usually the location of the center
More informationChapter 10.A. Rotation of Rigid Bodies
Chapter 10.A Rotation of Rigid Bodies P. Lam 7_23_2018 Learning Goals for Chapter 10.1 Understand the equations govern rotational kinematics, and know how to apply them. Understand the physical meanings
More informationMoment of Inertia Race
Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential
More informationAP Physics 1: Rotational Motion & Dynamics: Problem Set
AP Physics 1: Rotational Motion & Dynamics: Problem Set I. Axis of Rotation and Angular Properties 1. How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 2. How many degrees are
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 informationRotational Dynamics continued
Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2
More informationRotational Mechanics Part III Dynamics. Pre AP Physics
Rotational Mechanics Part III Dynamics Pre AP Physics We have so far discussed rotational kinematics the description of rotational motion in terms of angle, angular velocity and angular acceleration and
More informationRotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem
Slide 1 / 34 Rotational ynamics l Slide 2 / 34 Moment of Inertia To determine the moment of inertia we divide the object into tiny masses of m i a distance r i from the center. is the sum of all the tiny
More informationPS 11 GeneralPhysics I for the Life Sciences
PS 11 GeneralPhysics I for the Life Sciences ROTATIONAL MOTION D R. B E N J A M I N C H A N A S S O C I A T E P R O F E S S O R P H Y S I C S D E P A R T M E N T F E B R U A R Y 0 1 4 Questions and Problems
More informationRotational Motion About a Fixed Axis
Rotational Motion About a Fixed Axis Vocabulary rigid body axis of rotation radian average angular velocity instantaneous angular average angular Instantaneous angular frequency velocity acceleration acceleration
More informationTwoDimensional Rotational Kinematics
TwoDimensional Rotational Kinematics Rigid Bodies A rigid body is an extended object in which the distance between any two points in the object is constant in time. Springs or human bodies are nonrigid
More informationDEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B1A: ROTATIONAL DYNAMICS Essential Idea: The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual
More informationClassical Mechanics Lecture 15
Classical Mechanics Lecture 5 Today s Concepts: a) Parallel Axis Theorem b) Torque & Angular Acceleration Mechanics Lecture 5, Slide Unit 4 Main Points Mechanics Lecture 4, Slide Unit 4 Main Points Mechanics
More informationClass XI Chapter 7 System of Particles and Rotational Motion Physics
Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie
More informationAP Physics QUIZ Chapters 10
Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5kilogram sphere is connected to a 10kilogram sphere by a rigid rod of negligible
More informationHolt Physics Chapter 7. Rotational Motion
Holt Physics Chapter 7 Rotational Motion Measuring Rotational Motion Spinning objects have rotational motion Axis of rotation is the line about which rotation occurs A point that moves around an axis undergoes
More informationRotation Quiz II, review part A
Rotation Quiz II, review part A 1. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater angular velocity? A. A B. B C. C D. D E. All points have the
More informationReview for 3 rd Midterm
Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The momentofinertia about the centerofmass
More informationRolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1
Physics 131: Lecture Today s Agenda Rolling without slipping Angular Momentum Conservation o Angular Momentum Physics 01: Lecture 19, Pg 1 Rolling Without Slipping Rolling is a combination o rotation and
More informationRotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
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 9. Rotational Dynamics
Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular
More informationMoment of Inertia & Newton s Laws for Translation & Rotation
Moment of Inertia & Newton s Laws for Translation & Rotation In this training set, you will apply Newton s 2 nd Law for rotational motion: Στ = Σr i F i = Iα I is the moment of inertia of an object: I
More informationPhys101 Lectures 19, 20 Rotational Motion
Phys101 Lectures 19, 20 Rotational Motion Key points: Angular and Linear Quantities Rotational Dynamics; Torque and Moment of Inertia Rotational Kinetic Energy Ref: 101,2,3,4,5,6,8,9. Page 1 Angular Quantities
More informationChapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:
linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)
More informationUniform Circular Motion:Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant.
Circular Motion: Uniform Circular Motion:Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant. Angular Displacement: Scalar form:?s = r?θ Vector
More informationSuggested Problems. Chapter 1
Suggested Problems Ch1: 49, 51, 86, 89, 93, 95, 96, 102. Ch2: 9, 18, 20, 44, 51, 74, 75, 93. Ch3: 4, 14, 46, 54, 56, 75, 91, 80, 82, 83. Ch4: 15, 59, 60, 62. Ch5: 14, 52, 54, 65, 67, 83, 87, 88, 91, 93,
More information112 A General Method, and Rolling without Slipping
112 A General Method, and Rolling without Slipping Let s begin by summarizing a general method for analyzing situations involving Newton s Second Law for Rotation, such as the situation in Exploration
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 informationTorque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.
Warm up A remotecontrolled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics
More informationPhysics 131: Lecture 22. Today s Agenda
Physics 131: Lecture 22 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 An Unfair Race A frictionless block and a rolling (without slipping) disk are released
More informationRotational Kinematics and Dynamics. UCVTS AIT Physics
Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,
More informationReview questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.
Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the
More information16. Rotational Dynamics
6. Rotational Dynamics A Overview In this unit we will address examples that combine both translational and rotational motion. We will find that we will need both Newton s second law and the rotational
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF
More informationPhysics 4A Solutions to Chapter 10 Homework
Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 04 (a) positive (b) zero (c) negative (d) negative Q 06
More informationChapter 8  Rotational Dynamics and Equilibrium REVIEW
Pagpalain ka! (Good luck, in Filipino) Date Chapter 8  Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body
More informationPHYSICS 149: Lecture 21
PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30
More informationω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2
PHY 302 K. Solutions for problem set #9. Textbook problem 7.10: For linear motion at constant acceleration a, average velocity during some time interval from t 1 to t 2 is the average of the velocities
More informationMechanics II. Which of the following relations among the forces W, k, N, and F must be true?
Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which
More informationChapter 10: Dynamics of Rotational Motion
Chapter 10: Dynamics of Rotational Motion What causes an angular acceleration? The effectiveness of a force at causing a rotation is called torque. QuickCheck 12.5 The four forces shown have the same strength.
More informationQ1. For a completely inelastic twobody collision the kinetic energy of the objects after the collision is the same as:
Coordinator: Dr.. Naqvi Monday, January 05, 015 Page: 1 Q1. For a completely inelastic twobody collision the kinetic energy of the objects after the collision is the same as: ) (1/) MV, where M is the
More informationRotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart
Rotational Motion & Angular Momentum Rotational Motion Every quantity that we have studied with translational motion has a rotational counterpart TRANSLATIONAL ROTATIONAL Displacement x Angular Displacement
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationDynamics of Rotational Motion: Rotational Inertia
Dynamics of Rotational Motion: Rotational Inertia Bởi: OpenStaxCollege If you have ever spun a bike wheel or pushed a merrygoround, you know that force is needed to change angular velocity as seen in
More informationRotation. Rotational Variables
Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that
More informationPhysics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy
ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 89 pm in NSC 118/119 Sunday, 6:308 pm in CCLIR 468 Announcements This
More informationRelating Linear and Angular Kinematics. a rad = v 2 /r = rω 2
PH2213 : Advanced Examples from Chapter 10 : Rotational Motion NOTE: these are somewhat advanced examples of how we can apply the methods from this chapter, so are beyond what will be on the final exam
More informationPHY131H1S  Class 20. Preclass reading quiz on Chapter 12
PHY131H1S  Class 20 Today: Gravitational Torque Rotational Kinetic Energy Rolling without Slipping Equilibrium with Rotation Rotation Vectors Angular Momentum Preclass reading quiz on Chapter 12 1 Last
More informationBig Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1
Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50kg boy and a 40kg girl sit on opposite ends of a 3meter seesaw. How far from the girl should the fulcrum be placed in order for the
More informationRotational Motion. Rotational Motion. Rotational Motion
I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x =
More informationRotation review packet. Name:
Rotation review packet. Name:. A pulley of mass m 1 =M and radius R is mounted on frictionless bearings about a fixed axis through O. A block of equal mass m =M, suspended by a cord wrapped around the
More information1 Problems 13 A disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t
Slide 1 / 30 1 Problems 13 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s
More informationSlide 1 / 30. Slide 2 / 30. Slide 3 / m/s 1 m/s
1 Problems 13 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 1 / 30 etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s
More informationName: Date: Period: AP Physics C Rotational Motion HO19
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (99) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions
More informationPhysics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems
A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 E 4 rad, A) How many degrees is this B) How small an object can the bird just distinguish when flying
More informationMotion in Space. MATH 311, Calculus III. J. Robert Buchanan. Fall Department of Mathematics. J. Robert Buchanan Motion in Space
Motion in Space MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Background Suppose the position vector of a moving object is given by r(t) = f (t), g(t), h(t), Background
More informationPhysics 11 Fall 2012 Practice Problems 6
Physics 11 Fall 2012 Practice Problems 6 1. Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on
More information