PHYSICS

Part II: Mechanics

Hong Kong Diploma of Secondary Education

(HKDSE)

Notes & Exercises

Chapter 6 to 13

ANDY WONG S.T.

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TABLE OF CONTENTS

CHAPTER 6 KINEMATICS .............................................................................................................. 5

1. Introduction ..................................................................................................... 5

2. Scalars and vectors ....................................................................................... 5

3. Distance and displacement .......................................................................... 5

4. Speed and velocity......................................................................................... 5

5. Acceleration .................................................................................................... 5

6. Equations of uniformly accelerated motion ................................................ 5

7. String problem ................................................................................................ 5

8. Relative velocity ............................................................................................. 5

9. Graphical representation of displacement, velocity and acceleration ... 5

10. Vertical motion under gravity ........................................................................ 6

CHAPTER 7 NEWTON’S LAWS OF MOTION................................................................................... 7

1. Newton’s First Law of motion ....................................................................... 7

2. Force as vector ............................................................................................... 7

3. Newton’s Second Law of motion ................................................................. 7

4. Free-body diagrams....................................................................................... 7

5. Friction ............................................................................................................. 7

6. Force on inextensible string, spring and rigid rod ..................................... 7

7. Newton’s Third Law of motion – action and reaction pair ........................ 7

8. Mass and weight ............................................................................................ 7

9. Equilibrium of forces ...................................................................................... 8

CHAPTER 8 STATICS ..................................................................................................................... 9

1. Moment of a force (torque) ........................................................................... 9

2. Couples ............................................................................................................ 9

3. Static equilibrium of a rigid body .................................................................. 9

4. Static equilibrium of a body under three forces ......................................... 9

5. Centre of gravity (C.G.) and centre of mass .............................................. 9

6. Determination of C.G. of lamina – plumb line method ............................. 9

7. Determination of C.G. – mathematical method ......................................... 9

8. Stability** ......................................................................................................... 9

9. Equilibrium on an inclined plane ................................................................ 10

CHARTER 9 PROJECTILE MOTION .............................................................................................. 11

1. Free falling object ......................................................................................... 11

2. Terms relating to projectile motion ............................................................ 11

3. Elevation angle and range .......................................................................... 11

4. Independence of vertical and horizontal motions ................................... 11

CHAPTER 10 WORK, ENERGY AND POWER ............................................................................... 12

1. Mechanical work........................................................................................... 12

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2. Gravitational potential energy (P.E.) ......................................................... 12

3. Kinetic energy (K.E.) .................................................................................... 12

4. Law of conservation of energy ................................................................... 12

5. Power ............................................................................................................. 12

CHAPTER 11 MOMENTUM ........................................................................................................... 13

1. Momentum of a body ................................................................................... 13

2. Impulse and impulsive force ....................................................................... 13

3. Law of conservation of momentum ........................................................... 13

4. Types of collision .......................................................................................... 13

5. One-dimensional elastic collision .............................................................. 13

6. Elastic oblique collision ............................................................................... 13

7. Inertial frame and non-inertial frame** ...................................................... 13

*CHAPTER 12 CIRCULAR MOTION.............................................................................................. 14

1. Velocity and acceleration in circular motion ............................................ 14

2. Centripetal force ........................................................................................... 14

3. Vertical circular motion – object moving on a circular track .................. 14

4. Vertical circular motion – particle on a string ........................................... 14

5. Vertical circular motion – particle on a light rod ...................................... 14

6. Conical pendulum ........................................................................................ 14

7. Motion of a cyclist round a bend ................................................................ 14

8. Turning of a car around a level bend ........................................................ 14

9. Banked road for bicycle and car ................................................................ 15

10. Simplified analysis of a car turning around a level bend ....................... 15

11. Turning of aircraft in flight ........................................................................... 15

12. Does centrifugal force exist? ...................................................................... 15

13. Centrifuge ...................................................................................................... 15

14. Tangential component in circular motion ................................................. 15

*CHAPTER 13 GRAVITATION ...................................................................................................... 16

1. Newton’s law of gravitation ......................................................................... 16

2. Gravitational field (g-field) ........................................................................... 16

3. g-field inside and outside a thin hollow spherical shell .......................... 16

4. g-field inside and outside a uniform solid sphere .................................... 16

5. Elementary aerospace mechanics ............................................................ 16

6. Geosynchronous orbit for geostationary satellites .................................. 16

7. Variation of gravity with height** ................................................................ 16

**APPENDIX I SIMPLE HARMONIC MOTION ................................................................................ 17

1. Elastic spring................................................................................................. 17

2. Simple harmonic motion (S.H.M.) – horizontal spring model ................ 17

3. Energy stored in a spring ............................................................................ 17

4. Kinematics of S.H.M. ................................................................................... 17

5. Energy of a S.H.M. system ......................................................................... 17

6. Rotating phasor (vector) model for S.H.M. .............................................. 17

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7. Damped oscillation....................................................................................... 17

8. Forced oscillation ......................................................................................... 17

9. The Barton’s Pendulum............................................................................... 17

*These topics are not required in physics part of HKDSE Combined Science curriculum.

Part II

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CHAPTER 6

KINEMATICS

1. Introduction

2. Scalars and vectors

3. Distance and displacement

4. Speed and velocity

5. Acceleration

6. Equations of uniformly accelerated motion

7. String problem

8. Relative velocity

9. Graphical representation of displacement, velocity and acceleration

6

Displacement-time (s-t) graph

Velocity-time (v-t) graph

Acceleration-time (a-t) graph

10. Vertical motion under gravity

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CHAPTER 7

NEWTON’S LAWS OF MOTION

1. Newton’s First Law of motion

2. Force as vector

3. Newton’s Second Law of motion

4. Free-body diagrams

5. Friction

6. Force on inextensible string, spring and rigid rod

7. Newton’s Third Law of motion – action and reaction pair

8. Mass and weight

8

9. Equilibrium of forces

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CHAPTER 8

STATICS

1. Moment of a force (torque)

2. Couples

3. Static equilibrium of a rigid body

4. Static equilibrium of a body under three forces

5. Centre of gravity (C.G.) and centre of mass

6. Determination of C.G. of lamina – plumb line method

7. Determination of C.G. – mathematical method

8. Stability**

10

9. Equilibrium on an inclined plane

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CHARTER 9

PROJECTILE MOTION

1. Free falling object

2. Terms relating to projectile motion

3. Elevation angle and range

4. Independence of vertical and horizontal motions

12

CHAPTER 10

WORK, ENERGY AND POWER

1. Mechanical work

2. Gravitational potential energy (P.E.)

3. Kinetic energy (K.E.)

4. Law of conservation of energy

5. Power

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CHAPTER 11

MOMENTUM

1. Momentum of a body

2. Impulse and impulsive force

[from 2nd

law of motion]

3. Law of conservation of momentum

4. Types of collision

5. One-dimensional elastic collision

6. Elastic oblique collision

7. Inertial frame and non-inertial frame**

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*CHAPTER 12

CIRCULAR MOTION

1. Velocity and acceleration in circular motion

2. Centripetal force

3. Vertical circular motion – object moving on a circular track

4. Vertical circular motion – particle on a string

5. Vertical circular motion – particle on a light rod

6. Conical pendulum

7. Motion of a cyclist round a bend

8. Turning of a car around a level bend

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9. Banked road for bicycle and car

10. Simplified analysis of a car turning around a level bend

11. Turning of aircraft in flight

12. Does centrifugal force exist?

13. Centrifuge

14. Tangential component in circular motion

16

*CHAPTER 13

GRAVITATION

1. Newton’s law of gravitation

2. Gravitational field (g-field)

3. g-field inside and outside a thin hollow spherical shell

4. g-field inside and outside a uniform solid sphere

5. Elementary aerospace mechanics

6. Geosynchronous orbit for geostationary satellites

7. Variation of gravity with height**

Part II

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**APPENDIX I

SIMPLE HARMONIC MOTION

1. Elastic spring

2. Simple harmonic motion (S.H.M.) – horizontal spring model

3. Energy stored in a spring

4. Kinematics of S.H.M.

5. Energy of a S.H.M. system

6. Rotating phasor (vector) model for S.H.M.

7. Damped oscillation

Conclusions

8. Forced oscillation

9. The Barton’s Pendulum