Dynamics of Rotational Motion

Size: px
Start display at page:

Download "Dynamics of Rotational Motion"

Transcription

1 Dynamics of Rotational Motion Toque: the otational analogue of foce Toque = foce x moment am τ = l moment am = pependicula distance though which the foce acts a.k.a. leve am l l l l τ = l = sin φ = tan τ = Phys2C0 p Example: To loosen a difficult nut, a wench with a piece of pipe fo additional leveage is used. If the distance fom the cente of the nut to the end of the pipe is 0.80 m, and the wench and pipe make an angle of 20º with espect to the hoizontal, detemine the magnitude and diection of the toque applied by a 900 N man standing on the edge of the pipe. Phys2C0 p2

2 Toque and Angula Acceleation single paticle contibution,tan = m a sinceτ = τ = m α 2 i i Στ = Σm α = Iα i 2 Στ = Iα,tan,tan a,tan fo all component paticles : = α y-axis axis of otation,y,tan,ad Phys2C0 p3 Poblem solving tactics: Daw a diagam o each body, daw a fee body diagam Choose coodinates and diections (including fo otations) Relate toques to angula acceleations and foces to linea acceleations fo moe than one body, epeat and note any geometical elation between motions of bodies Phys2C0 p4

3 A cod is wapped aound a solid 50 kg cylinde which has a diamete of 0.20 m, and which otates (fictionlessly) about an axis though its cente. A 9.00 N foce is applied to the end of the cable, causing the cable to unwind and the dum (initially at est) to otate. What is the angula acceleation of the dum? 9.00 N A mass m is suspended by a sting wapped aound a pulley of adius R and moment of inetia I. The mass and pulley ae initially at est. Detemine the acceleation of the disk and of the suspended mass in tems of the given paametes (m, I, R). Examine the special case whee the pulley is a unifom disk of mass M. Phys2C0 p5 A mass m 2 is suspended by a sting wapped aound a pulley of adius R and moment of inetia I. The sting is then connected to a mass m which slides on a hoizontal fictionless suface. The masses and pulley ae initially at est. Detemine the acceleations of the masses and the pulley in tems of the the given paametes (m, m 2, I, R). Examine the special case whee the pulley can be teated as a thin cylindical shell of mass M. M m m 2 Phys2C0 p6

4 example: A pimitive yo-yo is made of a solid cylinde of mass M with sting wapped aound its adius R. What is the speed of the cylinde afte it has dopped a distance h? What is acceleation of the cylinde and the tension in the sting? example: A solid bowling bowl olls without slipping down a amp inclined at an angle β with espect to the hoizontal. What is the ball s acceleation? Phys2C0 p8

5 Rolling iction: defoming sufaces Stiff suface; nomal foce though cm, no toque Distoted suface; nomal foce offset fom cm, net toque slows otation Phys2C0 p9 Wok and Powe in Rotational Motion oce applied to a point on a otating object dw = W = tan = τdθ Rdθ τdθ W = τ θ when toque is constant R θ tan s tan Phys2C0 p0

6 dω τdθ = Iαdθ = I dθ = I dt W = τdθ = Iωdω = 2 W = Iω f Iω 2 2 dw dθ P = = τ dt dt P = τω 2 i dθ dω = Iωdω dt Wok - Enegy Powe Phys2C0 p If the powe output of an engine is 200 hp at 6000pm, what is the coesponding toque? A moto poduces a toque of 0 N-m with disk mounted to its shaft. The disk has a moment of inetia of 2.0 kg m 2. If the system stats fom est, detemine the wok done by the moto in 8.0 s, and the kinetic enegy of the disk at the end of this time. What is the aveage powe deliveed duing this 8 seconds? Phys2C0 p2

7 Angula momentum fo a single paticle, defined as L p = mv depends upon oigin! L = mv sinφ = mv = mv dl d dv = mv + m = v mv + ma dt dt dt dl = = τ dt L = Iω Genealize to composite object In the absence of extenal toques, angula momentum is conseved mv L mv φ ω Right hand ule fo diection Phys2C0 p3 Two disks with moments of inetia I a and I b shae a common axis of otation, but have diffeent angula velocities (ω a and ω b ). The disks ae bought togethe so that they eventually each a common final angula velocity. Deive an expession fo that final angula velocity ω. Suppose the two disks ae unifom with masses of 2.0 kg and 4.0 kg, adii of.20 m and.0 m and initial angula speeds of 50 ad/s and 200 ad/s. Detemine the final angula speed and the change in the kinetic enegy of the system. Phys2C0 p4

8 A bullet (0 g and initial speed 400 m/s) is fied into a doo fom a diection pependicula to the doo. The doo has a mass of 5 kg and is.0 m wide. Detemine the angula velocity of the doo afte the bullet embeds itself in the cente of the doo. Phys2C0 p5

9

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session. - 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU

More information

Physics C Rotational Motion Name: ANSWER KEY_ AP Review Packet

Physics C Rotational Motion Name: ANSWER KEY_ AP Review Packet Linea and angula analogs Linea Rotation x position x displacement v velocity a T tangential acceleation Vectos in otational motion Use the ight hand ule to detemine diection of the vecto! Don t foget centipetal

More information

Physics 1114: Unit 5 Hand-out Homework (Answers)

Physics 1114: Unit 5 Hand-out Homework (Answers) Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),

More information

Translation and Rotation Kinematics

Translation and Rotation Kinematics Tanslation and Rotation Kinematics Oveview: Rotation and Tanslation of Rigid Body Thown Rigid Rod Tanslational Motion: the gavitational extenal foce acts on cente-of-mass F ext = dp sy s dt dv total cm

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MAACHUETT INTITUTE OF TECHNOLOGY Depatment of Physics Physics 8. TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t = Exam 3: Equation ummay = Impulse: I F( t ) = p Toque: τ =,P dp F P τ =,P

More information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

Chapter 7-8 Rotational Motion

Chapter 7-8 Rotational Motion Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,

More information

Physics 201 Lecture 18

Physics 201 Lecture 18 Phsics 0 ectue 8 ectue 8 Goals: Define and anale toque ntoduce the coss poduct Relate otational dnamics to toque Discuss wok and wok eneg theoem with espect to otational motion Specif olling motion (cente

More information

Hoizontal Cicula Motion 1. A paticle of mass m is tied to a light sting and otated with a speed v along a cicula path of adius. If T is tension in the sting and mg is gavitational foce on the paticle then,

More information

Physics 111 Lecture 5 Circular Motion

Physics 111 Lecture 5 Circular Motion Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight

More information

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions ) 06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and

More information

Physics 111 Lecture 10. SJ 8th Ed.: Chap Torque, Energy, Rolling. Copyright R. Janow Spring basics, energy methods, 2nd law problems)

Physics 111 Lecture 10. SJ 8th Ed.: Chap Torque, Energy, Rolling. Copyright R. Janow Spring basics, energy methods, 2nd law problems) hysics Lectue 0 Toque, Enegy, Rolling SJ 8th Ed.: Chap 0.6 0.9 Recap and Oveview Toque Newton s Second Law fo Rotation Enegy Consideations in Rotational Motion Rolling Enegy Methods Second Law Applications

More information

b) (5) What average force magnitude was applied by the students working together?

b) (5) What average force magnitude was applied by the students working together? Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults

More information

Multiple choice questions [100 points] As shown in the figure, a mass M is hanging by three massless strings from the ceiling of a room.

Multiple choice questions [100 points] As shown in the figure, a mass M is hanging by three massless strings from the ceiling of a room. Multiple choice questions [00 points] Answe all of the following questions. Read each question caefully. Fill the coect ule on you scanton sheet. Each coect answe is woth 4 points. Each question has exactly

More information

AH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion

AH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed

More information

Chapters 5-8. Dynamics: Applying Newton s Laws

Chapters 5-8. Dynamics: Applying Newton s Laws Chaptes 5-8 Dynamics: Applying Newton s Laws Systems of Inteacting Objects The Fee Body Diagam Technique Examples: Masses Inteacting ia Nomal Foces Masses Inteacting ia Tensions in Ropes. Ideal Pulleys

More information

Principles of Physics I

Principles of Physics I Pinciples of Physics I J. M. Veal, Ph. D. vesion 8.05.24 Contents Linea Motion 3. Two scala equations........................ 3.2 Anothe scala equation...................... 3.3 Constant acceleation.......................

More information

Momentum is conserved if no external force

Momentum is conserved if no external force Goals: Lectue 13 Chapte 9 v Employ consevation of momentum in 1 D & 2D v Examine foces ove time (aka Impulse) Chapte 10 v Undestand the elationship between motion and enegy Assignments: l HW5, due tomoow

More information

PHYS 1410, 11 Nov 2015, 12:30pm.

PHYS 1410, 11 Nov 2015, 12:30pm. PHYS 40, Nov 205, 2:30pm. A B = AB cos φ x = x 0 + v x0 t + a 2 xt 2 a ad = v2 2 m(v2 2 v) 2 θ = θ 0 + ω 0 t + 2 αt2 L = p fs µ s n 0 + αt K = 2 Iω2 cm = m +m 2 2 +... m +m 2 +... p = m v and L = I ω ω

More information

Physics 101 Lecture 6 Circular Motion

Physics 101 Lecture 6 Circular Motion Physics 101 Lectue 6 Cicula Motion Assist. Pof. D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Equilibium, Example 1 q What is the smallest value of the foce F such that the.0-kg block will not slide

More information

Rectilinea Motion. A foce P is applied to the initially stationay cat. Detemine the velocity and displacement at time t=5 s fo each of the foce histoi

Rectilinea Motion. A foce P is applied to the initially stationay cat. Detemine the velocity and displacement at time t=5 s fo each of the foce histoi Rectilinea Motion 1. Small objects ae deliveed to the m inclined chute by a conveyo belt A which moves at a speed v 1 =0.4 m/s. If the conveyo belt B has a speed v =0.9 m/s and the objects ae deliveed

More information

PROBLEM (page 126, 12 th edition)

PROBLEM (page 126, 12 th edition) PROBLEM 13-27 (page 126, 12 th edition) The mass of block A is 100 kg. The mass of block B is 60 kg. The coefficient of kinetic fiction between block B and the inclined plane is 0.4. A and B ae eleased

More information

When a mass moves because of a force, we can define several types of problem.

When a mass moves because of a force, we can define several types of problem. Mechanics Lectue 4 3D Foces, gadient opeato, momentum 3D Foces When a mass moves because of a foce, we can define seveal types of poblem. ) When we know the foce F as a function of time t, F=F(t). ) When

More information

Quiz 6--Work, Gravitation, Circular Motion, Torque. (60 pts available, 50 points possible)

Quiz 6--Work, Gravitation, Circular Motion, Torque. (60 pts available, 50 points possible) Name: Class: Date: ID: A Quiz 6--Wok, Gavitation, Cicula Motion, Toque. (60 pts available, 50 points possible) Multiple Choice, 2 point each Identify the choice that best completes the statement o answes

More information

Experiment 09: Angular momentum

Experiment 09: Angular momentum Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MAACHUETT INTITUTE OF TECHNOLOGY Depatment of Physics Physics 8. TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t = Exam 3: Equation ummay = Impulse: I F( t ) = p Toque: τ =,P dp F P τ =,P

More information

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart Rotational Motion & Angula Momentum Rotational Motion Evey quantity that we have studied with tanslational motion has a otational countepat TRANSLATIONAL ROTATIONAL Displacement x Angula Position Velocity

More information

Lecture 13 EXAM 2. Today s Topics: Rotational motion Moment of inertia. Tuesday March 8, :15 PM 9:45 PM

Lecture 13 EXAM 2. Today s Topics: Rotational motion Moment of inertia. Tuesday March 8, :15 PM 9:45 PM Lectue 13 Rotational motion Moment of inetia EXAM uesday Mach 8, 16 8:15 PM 9:45 PM oday s opics: Rotational Motion and Angula Displacement Angula Velocity and Acceleation Rotational Kinematics Angula

More information

Lab 10: Newton s Second Law in Rotation

Lab 10: Newton s Second Law in Rotation Lab 10: Newton s Second Law in Rotation We can descibe the motion of objects that otate (i.e. spin on an axis, like a popelle o a doo) using the same definitions, adapted fo otational motion, that we have

More information

Lecture 13. Rotational motion Moment of inertia

Lecture 13. Rotational motion Moment of inertia Lectue 13 Rotational motion Moment of inetia EXAM 2 Tuesday Mach 6, 2018 8:15 PM 9:45 PM Today s Topics: Rotational Motion and Angula Displacement Angula Velocity and Acceleation Rotational Kinematics

More information

Section 26 The Laws of Rotational Motion

Section 26 The Laws of Rotational Motion Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to

More information

MAGNETIC FIELD INTRODUCTION

MAGNETIC FIELD INTRODUCTION MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),

More information

constant t [rad.s -1 ] v / r r [m.s -2 ] (direction: towards centre of circle / perpendicular to circle)

constant t [rad.s -1 ] v / r r [m.s -2 ] (direction: towards centre of circle / perpendicular to circle) VISUAL PHYSICS ONLINE MODULE 5 ADVANCED MECHANICS NON-UNIFORM CIRCULAR MOTION Equation of a cicle x y Angula displacement [ad] Angula speed d constant t [ad.s -1 ] dt Tangential velocity v v [m.s -1 ]

More information

Physics 181. Assignment 4

Physics 181. Assignment 4 Physics 181 Assignment 4 Solutions 1. A sphee has within it a gavitational field given by g = g, whee g is constant and is the position vecto of the field point elative to the cente of the sphee. This

More information

Wheel : MC, IC, rc. Pendulum : MB, IB, LB

Wheel : MC, IC, rc. Pendulum : MB, IB, LB In the figue, two cables of stiffness connect a wheel of mass M c to gound. The wheel with adius, has mass moment of inetia is I The pendulum, attached to the wheel cente, has mass M and mass moment of

More information

Physics 231 Lecture 21

Physics 231 Lecture 21 Physics 3 Lectue Main points o today s lectue: Angula momentum: L Newton s law o univesal gavitation: GMm F PE GMm Keple s laws and the elation between the obital peiod and obital adius. T π GM 4 3 Rolling

More information

to point uphill and to be equal to its maximum value, in which case f s, max = μsfn

to point uphill and to be equal to its maximum value, in which case f s, max = μsfn Chapte 6 16. (a) In this situation, we take f s to point uphill and to be equal to its maximum value, in which case f s, max = μsf applies, whee μ s = 0.5. pplying ewton s second law to the block of mass

More information

HW 7 Help. 60 s t. (4.0 rev/s)(1 min) 240 rev 1 min Solving for the distance traveled, we ll need to convert to radians:

HW 7 Help. 60 s t. (4.0 rev/s)(1 min) 240 rev 1 min Solving for the distance traveled, we ll need to convert to radians: HW 7 Help 30. ORGANIZE AND PLAN We ae given the angula velocity and the time, and we ae asked to ind the distance that is coveed. We can ist solve o the angula displacement using Equation 8.3: t. The distance

More information

( ) rad ( 2.0 s) = 168 rad

( ) rad ( 2.0 s) = 168 rad .) α 0.450 ω o 0 and ω 8.00 ω αt + ω o o t ω ω o α HO 9 Solution 8.00 0 0.450 7.8 b.) ω ω o + αδθ o Δθ ω 8.00 0 ω o α 0.450 7. o Δθ 7. ev.3 ev π.) ω o.50, α 0.300, Δθ 3.50 ev π 7π ev ω ω o + αδθ o ω ω

More information

A moving charged particle creates a magnetic field vector at every point in space except at its position.

A moving charged particle creates a magnetic field vector at every point in space except at its position. 1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units

More information

Department of Physics, Korea University Page 1 of 5

Department of Physics, Korea University Page 1 of 5 Name: Depatment: Student ID #: Notice ˆ + ( 1) points pe coect (incoect) answe. ˆ No penalty fo an unansweed question. ˆ Fill the blank ( ) with ( ) if the statement is coect (incoect). ˆ : coections to

More information

Physics 1A (a) Fall 2010: FINAL Version A 1. Comments:

Physics 1A (a) Fall 2010: FINAL Version A 1. Comments: Physics A (a) Fall 00: FINAL Vesion A Name o Initials: Couse 3-digit Code Comments: Closed book. No wok needs to be shown fo multiple-choice questions.. A helicopte is taveling at 60 m/s at a constant

More information

Physics 4A Chapter 8: Dynamics II Motion in a Plane

Physics 4A Chapter 8: Dynamics II Motion in a Plane Physics 4A Chapte 8: Dynamics II Motion in a Plane Conceptual Questions and Example Poblems fom Chapte 8 Conceptual Question 8.5 The figue below shows two balls of equal mass moving in vetical cicles.

More information

PHYS 2135 Exam I February 13, 2018

PHYS 2135 Exam I February 13, 2018 Exam Total /200 PHYS 2135 Exam I Febuay 13, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each Choose the best o most nealy coect answe Fo questions 6-9, solutions must begin

More information

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed?

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed? Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 10, 2012 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects

More information

Chapter 4. Newton s Laws of Motion

Chapter 4. Newton s Laws of Motion Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto

More information

PHYS 1114, Lecture 21, March 6 Contents:

PHYS 1114, Lecture 21, March 6 Contents: PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam

More information

Sections and Chapter 10

Sections and Chapter 10 Cicula and Rotational Motion Sections 5.-5.5 and Chapte 10 Basic Definitions Unifom Cicula Motion Unifom cicula motion efes to the motion of a paticle in a cicula path at constant speed. The instantaneous

More information

PHYSICS 151 Notes for Online Lecture #20

PHYSICS 151 Notes for Online Lecture #20 PHYSICS 151 Notes fo Online Lectue #20 Toque: The whole eason that we want to woy about centes of mass is that we ae limited to looking at point masses unless we know how to deal with otations. Let s evisit

More information

Chapter 4: The laws of motion. Newton s first law

Chapter 4: The laws of motion. Newton s first law Chapte 4: The laws of motion gavitational Electic magnetic Newton s fist law If the net foce exeted on an object is zeo, the object continues in its oiginal state of motion: - an object at est, emains

More information

Chapter 12. Kinetics of Particles: Newton s Second Law

Chapter 12. Kinetics of Particles: Newton s Second Law Chapte 1. Kinetics of Paticles: Newton s Second Law Intoduction Newton s Second Law of Motion Linea Momentum of a Paticle Systems of Units Equations of Motion Dynamic Equilibium Angula Momentum of a Paticle

More information

Construction Figure 10.1: Jaw clutches

Construction Figure 10.1: Jaw clutches CHAPTER TEN FRICTION CLUTCHES The wod clutch is a geneic tem descibing any one wide vaiety of devices that is capable of causing a machine o mechanism to become engaged o disengaged. Clutches ae of thee

More information

PHYSICS 1210 Exam 2 University of Wyoming 14 March ( Day!) points

PHYSICS 1210 Exam 2 University of Wyoming 14 March ( Day!) points PHYSICS 1210 Exam 2 Univesity of Wyoming 14 Mach ( Day!) 2013 150 points This test is open-note and closed-book. Calculatos ae pemitted but computes ae not. No collaboation, consultation, o communication

More information

r cos, and y r sin with the origin of coordinate system located at

r cos, and y r sin with the origin of coordinate system located at Lectue 3-3 Kinematics of Rotation Duing ou peious lectues we hae consideed diffeent examples of motion in one and seeal dimensions. But in each case the moing object was consideed as a paticle-like object,

More information

From Newton to Einstein. Mid-Term Test, 12a.m. Thur. 13 th Nov Duration: 50 minutes. There are 20 marks in Section A and 30 in Section B.

From Newton to Einstein. Mid-Term Test, 12a.m. Thur. 13 th Nov Duration: 50 minutes. There are 20 marks in Section A and 30 in Section B. Fom Newton to Einstein Mid-Tem Test, a.m. Thu. 3 th Nov. 008 Duation: 50 minutes. Thee ae 0 maks in Section A and 30 in Section B. Use g = 0 ms in numeical calculations. You ma use the following epessions

More information

Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun

Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law

More information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity

More information

AP-C WEP. h. Students should be able to recognize and solve problems that call for application both of conservation of energy and Newton s Laws.

AP-C WEP. h. Students should be able to recognize and solve problems that call for application both of conservation of energy and Newton s Laws. AP-C WEP 1. Wok a. Calculate the wok done by a specified constant foce on an object that undegoes a specified displacement. b. Relate the wok done by a foce to the aea unde a gaph of foce as a function

More information

Circular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK.

Circular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK. AP Physics C Sping, 2017 Cicula-Rotational Motion Mock Exam Name: Answe Key M. Leonad Instuctions: (92 points) Answe the following questions. SHOW ALL OF YOUR WORK. ( ) 1. A stuntman dives a motocycle

More information

Chapter 5. really hard to start the object moving and then, once it starts moving, you don t have to push as hard to keep it moving.

Chapter 5. really hard to start the object moving and then, once it starts moving, you don t have to push as hard to keep it moving. Chapte 5 Fiction When an object is in motion it is usually in contact with a viscous mateial (wate o ai) o some othe suface. So fa, we have assumed that moving objects don t inteact with thei suoundings

More information

Physics 107 TUTORIAL ASSIGNMENT #8

Physics 107 TUTORIAL ASSIGNMENT #8 Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type

More information

Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)

Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E) Geneal physics II (10) D. Iyad D. Iyad Chapte : lectic Fields In this chapte we will cove The lectic Field lectic Field Lines -: The lectic Field () lectic field exists in a egion of space suounding a

More information

Rigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018

Rigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018 Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining

More information

Central Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.

Central Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2. Cental oce Poblem ind the motion of two bodies inteacting via a cental foce. Cental oce Motion 8.01 W14D1 Examples: Gavitational foce (Keple poblem): 1 1, ( ) G mm Linea estoing foce: ( ) k 1, Two Body

More information

7.2.1 Basic relations for Torsion of Circular Members

7.2.1 Basic relations for Torsion of Circular Members Section 7. 7. osion In this section, the geomety to be consideed is that of a long slende cicula ba and the load is one which twists the ba. Such poblems ae impotant in the analysis of twisting components,

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Depatment of Physics and Engineeing Physics Physics 115.3 Physics and the Univese FINAL EXAMINATION Decembe 21, 2016 NAME: (Last) Please Pint (Given) Time: 3 hous STUDENT NO.:

More information

Potential Energy and Conservation of Energy

Potential Energy and Conservation of Energy Potential Enegy and Consevation of Enegy Consevative Foces Definition: Consevative Foce If the wok done by a foce in moving an object fom an initial point to a final point is independent of the path (A

More information

Conservation of Angular Momentum

Conservation of Angular Momentum 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 Consevation of Angula Momentum Pupose: To investigate consevation of angula momentum by diectly measuing the moment of inetia and angula velocities

More information

Kinematics of rigid bodies

Kinematics of rigid bodies Kinematics of igid bodies elations between time and the positions, elocities, and acceleations of the paticles foming a igid body. (1) Rectilinea tanslation paallel staight paths Cuilinea tanslation (3)

More information

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer. Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)

More information

CIRCULAR MOTION. Particle moving in an arbitrary path. Particle moving in straight line

CIRCULAR MOTION. Particle moving in an arbitrary path. Particle moving in straight line 1 CIRCULAR MOTION 1. ANGULAR DISPLACEMENT Intoduction: Angle subtended by position vecto of a paticle moving along any abitay path w..t. some fixed point is called angula displacement. (a) Paticle moving

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights

More information

b) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block?

b) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block? Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 13, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to

More information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

More information

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE.

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE. Unit 6 actice Test 1. Which one of the following gaphs best epesents the aiation of the kinetic enegy, KE, and of the gaitational potential enegy, GE, of an obiting satellite with its distance fom the

More information

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits Poblem Set 5: Univesal Law of Gavitation; Cicula Planetay Obits Design Engineeing Callenge: Te Big Dig.007 Contest Evaluation of Scoing Concepts: Spinne vs. Plowe PROMBLEM 1: Daw a fee-body-diagam of a

More information

Chapter 2: Basic Physics and Math Supplements

Chapter 2: Basic Physics and Math Supplements Chapte 2: Basic Physics and Math Supplements Decembe 1, 215 1 Supplement 2.1: Centipetal Acceleation This supplement expands on a topic addessed on page 19 of the textbook. Ou task hee is to calculate

More information

Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j.

Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j. 7. We denote the two foces F A + F B = ma,sof B = ma F A. (a) In unit vecto notation F A = ( 20.0 N)ˆ i and Theefoe, Phys 201A Homewok 6 Solutions F A and F B. Accoding to Newton s second law, a = [ (

More information

Rotatoy Motion Hoizontal Cicula Motion In tanslatoy motion, evey point in te body follows te pat of its pecedin one wit same velocity includin te cente of mass In otatoy motion, evey point move wit diffeent

More information

Easy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is

Easy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is Chapte 8 Homewok Solutions Easy P8. Assume the velocity of the blood is constant ove the 0.60 s. Then the patient s body and pallet will have a constant velocity of 6 0 5 m 3.75 0 4 m/ s 0.60 s in the

More information

Physics 111 Lecture 12. SJ 8th Ed.: Chap Static Equilibrium. Overview - Equilibrium Defined. Static Equilibrium Examples

Physics 111 Lecture 12. SJ 8th Ed.: Chap Static Equilibrium. Overview - Equilibrium Defined. Static Equilibrium Examples Physics 111 ectue 1 Static Equilibium SJ 8th Ed.: Chap 1.1 1.3 Oveview - Equilibium Defined Conditions fo Equilibium Cente of Gavity Defined inding it When do mass cente and CG not coincide? Static Equilibium

More information

Uniform Circular Motion

Uniform Circular Motion Unifom Cicula Motion Intoduction Ealie we defined acceleation as being the change in velocity with time: a = v t Until now we have only talked about changes in the magnitude of the acceleation: the speeding

More information

1121 T Question 1

1121 T Question 1 1121 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, tavelling on the sae path in the sae diection as you, at a constant speed

More information

16.1 Permanent magnets

16.1 Permanent magnets Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and

More information

Magnetic Dipoles Challenge Problem Solutions

Magnetic Dipoles Challenge Problem Solutions Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom

More information

Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here.

Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here. Physics 07: Lecture 4 Announcements No labs next week, May 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here Today s Agenda ecap: otational dynamics and torque Work and energy with example Many

More information

Chapter 1: Mathematical Concepts and Vectors

Chapter 1: Mathematical Concepts and Vectors Chapte : Mathematical Concepts and Vectos giga G 9 mega M 6 kilo k 3 centi c - milli m -3 mico μ -6 nano n -9 in =.54 cm m = cm = 3.8 t mi = 58 t = 69 m h = 36 s da = 86,4 s ea = 365.5 das You must know

More information

The Laws of Motion ( ) N SOLUTIONS TO PROBLEMS ! F = ( 6.00) 2 + ( 15.0) 2 N = 16.2 N. Section 4.4. Newton s Second Law The Particle Under a Net Force

The Laws of Motion ( ) N SOLUTIONS TO PROBLEMS ! F = ( 6.00) 2 + ( 15.0) 2 N = 16.2 N. Section 4.4. Newton s Second Law The Particle Under a Net Force SOLUTIONS TO PROBLEMS The Laws of Motion Section 4.3 Mass P4. Since the ca is moving with constant speed and in a staight line, the esultant foce on it must be zeo egadless of whethe it is moving (a) towad

More information

PHYSICS NOTES GRAVITATION

PHYSICS NOTES GRAVITATION GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely

More information

Moment. F r F r d. Magnitude of moment depends on magnitude of F and the length d

Moment. F r F r d. Magnitude of moment depends on magnitude of F and the length d Moment Tanslation Tanslation + Rotation This otation tenency is known as moment M of foce (toque) xis of otation may be any line which neithe intesects no paallel to the line of action of foce Magnitue

More information

Chapter 8. Accelerated Circular Motion

Chapter 8. Accelerated Circular Motion Chapte 8 Acceleated Cicula Motion 8.1 Rotational Motion and Angula Displacement A new unit, adians, is eally useful fo angles. Radian measue θ(adians) = s = θ s (ac length) (adius) (s in same units as

More information

Lecture 19 Angular momentum. Chapter

Lecture 19 Angular momentum. Chapter PHYS 172H: Moden Mechanics Fall 2010 Lectue 19 ngula momentum Chapte 11.4 11.7 The angula momentum pinciple dp = F dl =? net d ( p ) d dp = p+ = v γ mv = = 0 The angula momentum pinciple fo a point paticle

More information

Newton s Laws, Kepler s Laws, and Planetary Orbits

Newton s Laws, Kepler s Laws, and Planetary Orbits Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion

More information

Physics 11 Chapter 4: Forces and Newton s Laws of Motion. Problem Solving

Physics 11 Chapter 4: Forces and Newton s Laws of Motion. Problem Solving Physics 11 Chapte 4: Foces and Newton s Laws of Motion Thee is nothing eithe good o bad, but thinking makes it so. William Shakespeae It s not what happens to you that detemines how fa you will go in life;

More information

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1

PROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1 PROBLEM SET #3A AST242 Figue 1. Two concentic co-axial cylindes each otating at a diffeent angula otation ate. A viscous fluid lies between the two cylindes. 1. Couette Flow A viscous fluid lies in the

More information

Physics 1A (b) Fall 2010: FINAL Version A 1. Comments:

Physics 1A (b) Fall 2010: FINAL Version A 1. Comments: Physics A (b) Fall 00: FINAL Vesion A Name o Initials: Couse 3-digit Code Comments: Closed book. No wok needs to be shown fo multiple-choice questions.. An 80 kg man is one fouth of the way up a 0 m ladde

More information

Physics. Rotational Motion.

Physics. Rotational Motion. Physics otational Motion www.testpepat.com Table of Content. Intoduction.. Cente of Mass.. Angula Displacement. 4. Angula Velocity.. Angula Acceleation. 6. Equations of Linea Motion and otational Motion.

More information

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D. ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic

More information