A MEMOIR BY MATTHEW SANDS 1
1 Prerequisites 15
REVIEW LECTURE A 15
1-1 Introduction to the review lecture 15
1-2 Caltech from the bottom 16
1-3 Mathematics for physics 18
1-4 Differentiation 19
1-5 Integration 22
1-6 Vectors 23
1-7 Differentiating vectors 29
1-8 Line integrals 31
1-9 A simple example 33
1-10 Triangulation 38
2 Laws and Intuition 41
REVIEW LECTURE B 41
2-1 The physical laws 41
2-2 The nonrelativistic approximation 43
2-3 Motion with forces 44
2-4 Forces and their potentials 47
2-5 Learning physics by example 49
2-6 Understanding physics physically 50
2-7 A problem in machine design 53
2-8 Earth’s escape velocity 64
Alternate Solutions 67
A Finding the acceleration of the weight using geometry 67
B Finding the acceleration of the weight using trigonometry 68
C Finding the force on the weight using torque and angular momentum 69
3 Problems and Solutions 71
REVIEW LECTURE C 71
3-1 Satellite motion 71
3-2 Discovery of the atomic nucleus 76
3-3 The fundamental rocket equation 80
3-4 A numerical integration 82
3-5 Chemical rockets 84
3-6 Ion propulsion rockets 85
3-7 Photon propulsion rockets 88
3-8 An electrostatic proton beam deflector 88
3-9 Determining the mass of the pi meson 91
4 Dynamical Effects and Their Applications 96
4-1 A demonstration gyroscope 96
4-2 The directional gyro 97
4-3 The artificial horizon 98
4-4 A ship-stabilizing gyroscope 99
4-5 The gyrocompass 100
4-6 Improvements in gyroscopes design and construction 104
4-7 Accelerometers 111
4-8 A complete navigational system 115
4-9 Effects of the earth’s rotation 119
4-10 The spinning disk 122
4-11 Earth’s nutation 125
4-12 Angular momentum in astronomy 125
4-13 Angular momentum in quantum mechanics 127
4-14 After the lecture 128
5 Selected Exercises 135
5-1 Conservation of energy，statics 135
5-2 Kepler’s laws and gravitation 138
5-3 Kinematics 138
5-4 Newton’s laws 139
5-5 Conservation of momentum 141
5-6 Vectors 143
5-7 Nonrelativistic two-body collisions in 3 dimensions 144
5-8 Forces 144
5-9 Potentials and fields 145
5-10 Units and dimensions 147
5-11 Relativistic energy and momentum 147
5-12 Rotations in two dimensions，the center mass 148
5-13 Angular momentum，the moment of inertia 149
5-14 Rotation in three dimensions 151
Answers to Exercises 155
Photo Credits 159
Index to The Lectures 161