ENGR-226-01 MECHANICS II WEEK # 1 INTRODUCTION ------------ 1.- INTRODUCTION TO THE COURSE 1.1.- COURSE OBJECTIVE AND CONTENTS 1.2.- HOMEWORK, EXAMS AND STUDY GROUP 1.3.- COURSE OUTLINE * DYNAMICS (KINEMATICS AND KINETICS) OF PARTICLES @ SINGLE PARTICLES @ SYSTEMS OF PARTICLES * DYNAMICS (KINEMATICS AND KINETICS) OF RIGID BODIES @ PLANAR SYSTEMS @ SPATIAL SYSTEMS 2.- BASIC CONCEPTS, UNITS AND DIMENSIONS 2.1.- TIME, MASS, FORCE, PARTICLES AND RIGID BODIES 2.2.- SCALARS AND VECTORS 2.3.- NEWTON'S LAWS 2.4.- UNITS (EMPHASIZING S.I. SYSTEM) AND DIMENSIONS HOMEWORK ASSIGNMENT REVIEW: APPENDICES C1-C10; PREFACE TO THE STUDENT; CHAPTER 1 ENGR-226-01 MECHANICS II WEEK # 2 KINEMATICS OF A PARTICLE: LINEAR AND PLANAR MOTIONS --------------------------------------------------- 1.- KINEMATICS OF A PARTICLE: RECTILINEAR MOTION 1.1.- CONSTRAINED AND UNCONSTRAINED MOTION OF A PARTICLE 1.2.- ABSOLUTE AND RELATIVE MOTIONS: REFERENCE AXES 1.3.- RECTILINEAR MOTION * DISPLACEMENT * VELOCITY * ACCELERATION * INTEGRATION OF EQUATIONS & CONSTANT ACCELERATION & ACCELERATION AS FUNCTION OF TIME & ACCELERATION AS FUNCTION OF VELOCITY & ACCELERATION AS FUNCTION OF DISPLACEMENT 2.- PLANE CURVILINEAR MOTION 2.1.- POSITION VECTOR OF A PARTICLE 2.2.- TIME RATE OF CHANGE OF POSITION VECTOR (VELOCITY VECTOR) 2.3.- MAGNITUDE OF THE VELOCITY VECTOR (SPEED) 2.4.- TIME RATE OF CHANGE OF VELOCITY VECTOR (ACCELERATION VECTOR) 2.5.- HODOGRAPH 3.- SYSTEMS OF COORDINATES 3.1.- RECTANGULAR COORDINATES * COMPONENT NOTATION FOR POSITION, VELOCITY AND ACCELERATION VECTORS IN TWO-DIMENSIONAL MOTIONS * MAGNITUDES OF MOTION VECTORS 3.2.- NORMAL AND TANGENTIAL COORDINATES * COMPONENT NOTATION FOR POSITION, VELOCITY AND ACCELERATION VECTORS IN TWO-DIMENSIONAL MOTIONS * MAGNITUDES OF MOTION VECTORS 3.3.- POLAR COORDINATES * COMPONENT NOTATION FOR POSITION, VELOCITY AND ACCELERATION VECTORS IN TWO-DIMENSIONAL MOTIONS * MAGNITUDES AND DIRECTION CHANGES OF MOTION VECTORS HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 2.1 - 2.10 ATTEMPT: PROBLEMS 2.26; 2.31; 2.54; 2.82; 2.90; 2.95, 2.128; 2.163 ENGR-226-01 MECHANICS II WEEK # 3 KINEMATICS OF A PARTICLE: SPATIAL, RELATIVE AND CONSTRAINED MOTION ------------------------------------------------------------------- 1.- SPACE CURVILINEAR MOTION 1.1.- RECTANGULAR COORDINATES 1.2.- CYLINDRICAL COORDINATES 1.3.- SPHERICAL COORDINATES 2.- RELATIVE MOTION 2.1.- MEASURING POSITION WITH RESPECT TO FIXED AND MOVING SYSTEMS OF COORDINATES 2.2.- RELATIVE MOTION OF A TRANSLATIONAL REFERENCE SYSTEM * RELATIVE AND ABSOLUTE POSITION VECTORS * RELATIVE AND ABSOLUTE VELOCITIES * RELATIVE AND ABSOLUTE ACCELERATIONS 2.3.- INERTIAL SYSTEM OF REFERENCE 3.- CONSTRAINED MOTION OF CONNECTED PARTICLES 3.1.- SYSTEMS WITH ONE DEGREE OF FREEDOM 3.2.- SYSTEMS WITH TWO DEGREES OF FREEDOM HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 2.11-15 ATTEMPT: PROBLEMS 2.170, 2.176, 2.190, 2.200, 2.218, 2.239 ENGR-226-01 MECHANICS II WEEK # 4 KINETICS OF A PARTICLE: FORCE, MASS AND ACCELERATION ---------------------------------------------------- 1.- INTRODUCTION 1.1.- NEWTON'S SECOND LAW: F = m a 1.2.- EQUATION OF MOTION 2.- THE TWO TYPES OF PROBLEMS OF DYNAMICS 2.1.- GIVEN THE MOTION, FIND THE FORCE(S) 2.2.- GIVEN THE FORCE(S), FIND THE MOTION 3.- FREE-BODY DIAGRAMS 4.- TWO COMMON TYPES OF MOTION 4.1.- RECTILINEAR MOTION 4.2.- CURVILINEAR MOTION HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 3.1-3.10 ATTEMPT: PROBLEMS 3.7, 3.14, 3.42, 3.59, 3.72, 3.94 ENGR-226-01 MECHANICS II WEEK # 5 KINETICS OF A PARTICLE: WORK AND ENERGY; IMPULSE AND MOMENTUM ------------------------------------------------------------- 1.- WORK AND KINETIC ENERGY 1.1.- WORK 1.2.- KINETIC ENERGY 1.3.- WORK-ENERGY EQUATION 1.4.- POWER 1.5.- EFFICIENCY 2.- POTENTIAL ENERGY 2.1.- TWO TYPES OF POTENTIAL ENERGY * GRAVITATIONAL POTENTIAL ENERGY * ELASTIC POTENTIAL ENERGY 2.2.- WORK-ENERGY EQUATION REVISITED * TOTAL MECHANICAL ENERGY * LAW OF CONSERVATION OF DYNAMICAL ENERGY 2.3.- CONSERVATIVE AND NON-CONSERVATIVE FORCE FIELDS 3.- IMPULSE AND MOMENTUM 3.1.- LINEAR MOMENTUM AND LINEAR IMPULSE * LINEAR MOMENTUM OF A PARTICLE * LINEAR IMPULSE OF A FORCE * TOTAL LINEAR IMPULSE = CHANGE IN LINEAR MOMENTUM 3.2.- ANGULAR MOMENTUM AND ANGULAR IMPULSE * ANGULAR MOMENTUM ( = MOMENT OF MOMENTUM) OF A PARTICLE * TORQUE (= MOMENT OF FORCE) * ANGULAR IMPULSE OF A FORCE * TOTAL ANGULAR IMPULSE = CHANGE IN ANGULAR MOMENTUM 3.3.- CONSERVATION OF MOMENTUM * CONSERVATION OF LINEAR MOMENTUM * CONSERVATION OF ANGULAR MOMENTUM HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 3.11-3.23 ATTEMPT: PROBLEMS 3.113; 3.158; 3.208; 3.222; 3.230 ENGR-226-01 MECHANICS II WEEK # 6 READING WEEK ------------ READ SECTIONS 3.1 TO 3.15 FROM YOUR TEXTBOOK ENGR-226-01 MECHANICS II WEEK # 7 KINETICS OF A PARTICLE: SOME APPLICATIONS ----------------------------------------- 1.- SOME APPLICATIONS OF PARTICLE KINETICS 1.1.- REVIEW OF BASIC PRINCIPLES AND METHODS OF KINETICS 1.2.- IMPACT PROBLEMS * DIRECT CENTRAL IMPACT * COEFFICIENT OF RESTITUTION * OBLIQUE CENTRAL IMPACT 1.3.- CENTRAL FORCE MOTION * KEPLER'S LAWS OF PLANETARY MOTION * "PERTURBED" TWO-BODY PROBLEM 1.4.- RELATIVE MOTION * RELATIVE MOTION EQUATIONS * D'ALEMBERT'S PRINCIPLE * CONSTANT VELOCITY TRANSLATING SYSTEMS HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 3.24-3.29 ATTEMPT: PROBLEMS 3.246; 3.258; 3.270; 3.288; 3.305; 3.311; ENGR-226-01 MECHANICS II WEEK # 8 KINETICS OF MULTIPARTICLE SYSTEMS --------------------------------- 1.- COMPARING SINGLE PARTICLE SYSTEMS WITH MULTIPARTICLE SYSTEMS 2.- TYPES OF FORCES ACTING ON A PARTICLE WHICH IS MEMBER OF A MULTIPARTICLE ASSEMBLY 2.1.- EXTERNAL 2.2.- INTERNAL 3.- DYNAMICAL EQUATION FOR MULTIPARTICLE SYSTEMS 3.1.- DYNAMICAL EQUATION FOR A SINGLE PARTICLE IN THE ASSEMBLY 3.2.- DYNAMICAL EQUATION FOR THE ASSEMBLY: PRINCIPLE OF MOTION OF THE MASS CENTER 4.- WORK AND ENERGY OF MULTIPARTICLE SYSTEMS 4.1.- WORK, ENERGY AND ENERGY EQUATION FOR A SINGLE PARTICLE IN THE ASSEMBLY 4.2.- WORK, ENERGY AND ENERGY EQUATION FOR THE WHOLE ASSEMBLY 4.3.- CONSERVATION OF ENERGY IN MULTIPARTICLE SYSTEMS 5.- MOMENTUM AND IMPULSE IN MULTIPARTICLE SYSTEMS 5.1.- LINEAR MOMENTUM * FORCES AND THE TIME RATE OF CHANGE OF LINEAR MOMENTUM 5.2.- ANGULAR MOMENTUM * ABOUT O * ABOUT G * ABOUT P * TORQUES AND TIME RATE OF CHANGE OF ANGULAR MOMENTUM 5.3.- CONSERVATION OF MOMENTUM IN MULTIPARTICLE SYSTEMS 6.- ADDITIONAL EXAMPLES OF MULTIPARTICLE KINETICS HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 4.1-4.11 ATTEMPT: PROBLEMS 4.6; 4.22; 4.39 ENGR-226-01 MECHANICS II WEEK # 9 PLANE KINEMATICS OF RIGID BODIES: --------------------------------- ROTATION, ABSOLUTE AND RELATIVE MOTION -------------------------------------- 1.- INTRODUCTION 1.1.- CONCEPT OF RIGID BODY 1.2.- TYPES OF PLANE MOTION OF A RIGID BODY * TRANSLATION (RECTILINEAR AND CURVILINEAR) * ROTATION * GENERAL 2.- ROTATION 2.1.- ROTATION OF A RIGID BODY 2.2.- ANGULAR MOTION RELATIONS 2.3.- ROTATION ABOUT A FIXED AXIS 3.- ABSOLUTE MOTION ANALYSIS 4.- RELATIVE MOTION ANALYSIS 4.1.- RELATIVE LINEAR MOTION AND ABSOLUTE ANGULAR MOTION 4.2.- RELATIVE LINEAR VELOCITY 5.- INSTANTANEOUS CENTER OF ZERO VELOCITY HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 5.1-5.12 ATTEMPT: PROBLEMS 5.16; 5.44; 5.76 ENGR-226-01 MECHANICS II WEEK # 10 PLANE KINEMATICS OF RIGID BODIES: --------------------------------- RELATIVE ACCELERATION; ROTATING AXES ------------------------------------ 1.- RELATIVE ACCELERATION (OF POINT A) 1.1.- aA = aB + aA/B|n + aA/B|t 1.2.- aA/B|n = wX(wXr) 1.3.- aA/B|t = (dw/dt)Xr 2.- MOTION RELATIVE TO ROTATING AXES 2.1.- MOTION OF A POINT WITH RESPECT TO A ROTATING RECTANGULAR CARTESIAN SYSTEM OF COORDINATES 2.2.- POSITION VECTOR (OF POINT A) rA = rB + r 2.3.- TIME DERIVATIVES OF UNIT VECTORS i AND j di/dt = wXi; dj/dt = wXj 2.4.- RELATIVE VELOCITY (OF POINT A) vA = vB + vR + wXr 2.5.- TIME DERIVATIVE OF A VECTOR F dF/dt|XY = dF/dt|xy + wXF 2.6.- RELATIVE ACCELERATION (OF POINT A) aA = aB + (dw/dt)Xr + wX(wXr) + 2 wXvR + aR HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEMS 5.13-5.18 ATTEMPT: PROBLEMS 5.128, 5.134, 5.168, 5.173 ENGR-226-01 MECHANICS II WEEK # 11 PLANE KINETICS OF RIGID BODIES: ------------------------------- FORCE, MASS AND ACCELERATION ---------------------------- 1.- SYSTEM, BOUNDARY AND SURROUNDINGS 2.- FORCE MASS AND ACCELERATION 2.1.- DYNAMIC EQUATION IN TERMS OF FORCE 2.2.- ANGULAR MOMENTUM AND MASS MOMENT OF INERTIA 2.3.- TORQUE ANGULAR MOMENTUM RELATIONSHIP 2.4.- TORQUE ANGULAR MOMENTUM RELATIONSHIP (w.r.t. P ) 2.5.- EXAMPLES OF COMMON RIGID BODY MOTIONS * UNCONSTRAINED AND CONSTRAINED MOTION * INTERCONNECTED BODIES 2.6.- SOME IMPORTANT PLANE MOTIONS OF A RIGID BODY * TRANSLATION * FIXED AXIS ROTATION * GENERAL PLANE MOTION HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEM 6.1-6.8 ATTEMPT: PROBLEMS 6.11, 6.25, 6.53, 6.75, 6.89 ENGR-226-01 MECHANICS II WEEK # 12 SPRING VACATION --------------- WEEK # 13 PLANE KINETICS OF RIGID BODIES: ------------------------------- WORK AND ENERGY --------------- 1.- WORK OF FORCES AND COUPLES 2.- KINETIC ENERGY 2.1.- TRANSLATION 2.2.- FIXED AXIS ROTATION 2.3.- GENERAL PLANE MOTION 3.- POTENTIAL ENERGY 4.- POWER HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEM 6.9-6.13 ATTEMPT: PROBLEMS 6.134; 6.154; 6.160; 6.183 ENGR-226-01 MECHANICS II WEEK # 13 PLANE KINETICS OF RIGID BODIES: ------------------------------- WORK AND ENERGY --------------- 1.- WORK OF FORCES AND COUPLES 2.- KINETIC ENERGY 2.1.- TRANSLATION 2.2.- FIXED AXIS ROTATION 2.3.- GENERAL PLANE MOTION 3.- POTENTIAL ENERGY 4.- POWER HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEM 6.9-6.13 ATTEMPT: PROBLEMS 6.134; 6.154; 6.160; 6.183 ENGR-226-01 MECHANICS II WEEK # 14 PLANE KINETICS OF RIGID BODIES: ------------------------------- IMPULSE AND MOMENTUM -------------------- 1.- LINEAR MOMENTUM 2.- ANGULAR MOMENTUM 3.- INTERCONNECTED BODIES 4.- MOMENTUM CONSERVATION 5.- IMPACT PHENOMENA HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEM 6.14-6.16 ENGR-226-01 MECHANICS II WEEK # 15 SPATIAL DYNAMICS OF RIGID BODIES -------------------------------- 1.- THE NEED FOR A VECTOR TREATMENT 2.- KINEMATICS OF SOME SIMPLE MOTIONS 2.1.- TRANSLATION 2.2.- FIXED AXIS ROTATION 2.3.- PARALLEL PLANE MOTION 2.4.- 3D ROTATION ABOUT A FIXED POINT AND INSTANTANEOUS AXIS OF ROTATION 3.- KINEMATICS OF GENERAL 3D MOTION 3.1.- SYSTEM OF REFERENCES TRANSLATES ONLY 3.2.- SYSTEM OF REFERENCE TRANSLATES AND ROTATES 3.3.- TIME DERIVATIVE OF ANY VECTOR 4.- KINETICS 4.1.- ANGULAR MOMENTUM 4.2.- KINETIC ENERGY 4.3.- MOMENTUM AND ENERGY EQUATIONS 5.- KINETICS OF SOME COMPLEX 3D MOTIONS 5.1.- PARALLEL PLANE MOTION 5.2.- GYROSCOPIC MOTION HOMEWORK ASSIGNMENT REVIEW: SAMPLE PROBLEM 7.1-7.9 ATTEMPT: PROBLEMS