Chapter 1	-  -

Physics 121		Chapter 1

TABLE OF CONTENTS

1.	UNITS	1

2.	MOTION IN A STRAIGHT LINE	3
2.1.	Position	3
2.2.	Velocity	4
2.3.	Acceleration	6
2.4.	Constant Acceleration	7
2.5.	Gravitational Acceleration	9

3.	VECTORS	13
3.1.	Vector Addition	13
3.1.1.	The graphical method	13
3.1.2.	The analytical method	15
3.2.	Multiplying Vectors  -  Multiplying a Vector by a Scalar	18
3.3.	Multiplying Vectors  -  Scalar Product	18
3.4.	Multiplying Vectors  -  Vector Product	20

4.	Motion in a Plane	23
4.1.	Position	23
4.2.	Velocity	23
4.3.	Acceleration	24
4.4.	Projectile Motion	27
4.5.	Circular Motion	33
4.6.	Relative Motion in 1D	35
4.7.	Relative Motion in 2D	38

5.	Force and Motion  -  1	41
5.1.	Newton’s First Law	41
5.2.	Force	42
5.3.	Newton’s Third Law	45
5.4.	Mass and Weight	46
5.4.1.	Measuring Mass	46
5.4.2.	Measuring Weight	47
5.5.	Applications	47

6.	Force and Motion - II	55
6.1.	Static and Kinetic Friction	55
6.2.	Drag Force	62
6.3.	Uniform Circular Motion	64
6.4.	Rounding a Curve	65

7.	Work and Kinetic Energy	73
7.1.	Work:  constant force	73
7.2.	Work:  variable force	78
7.3.	Work in 2D	80
7.4.	Kinetic Energy	82
7.5.	Power	85

8.	The Conservation of Energy	87
8.1.	Conservation laws	87
8.2.	Conservation of mechanical energy	87
8.2.1.	The spring force	88
8.2.2.	Gravitational force	91
8.2.3.	Friction force	92
8.3.	Conservative and non-conservative forces	92
8.4.	Potential energy curve	94
8.5.	Non-conservative forces	94
8.6.	Conservation of energy	95

9.	Systems of Particles	99
9.1.	Center of mass	99
9.2.	Motion of the Center of Mass	103
9.3.	Linear Momentum	106
9.4.	The rocket	112

10.	Collisions	115
10.1.	Introduction	115
10.2.	Impulse	115
10.3.	Collisions in One-Dimension	116
10.5.	Motion of the Center of Mass	119
10.6.	Collisions in One-Dimension: Inelastic	121
10.7.	Collisions in Two-Dimensions	124

11.	Rotation	129
11.1.	Rotational variables	129
11.2.	Constant angular acceleration	131
11.3.	Relation between linear and angular variables	132
11.4.	Kinetic energy of rotation	133
11.5.	Calculation of rotational inertia	134
11.6.	Torque	136
11.7.	Work	139

12.	Rolling, Torque and Angular Momentum	141
12.1.	Rolling Motion	141
12.2.	Kinetic Energy	142
12.3.	Torque	147
12.4.	Angular Momentum	147
12.5.	Angular Momentum of Rotating Rigid Bodies	150
12.6.	Conservation of Angular Momentum	151
12.7.	The Precessing Top	153

13.	Equilibrium and Elasticity	155
13.1.	Equilibrium	155
13.2.	Requirements for Equilibrium	155
13.3.	Equilibrium and the Force of Gravity	156
13.4.	Stacking Blocks	160

14.	Oscillations	163
14.1.	Simple Harmonic Motion	163
14.2.	Damped Simple Harmonic Motion	172
14.3.	Driven Harmonic Motion	174

15.	Gravity	177
15.1.	The Gravitational Force	177
15.2.	The gravitational constant G	179
15.3.	Free-fall Acceleration	180
15.4.	Gravitational Potential Energy	182
15.5.	Motion of planets	185
15.6.	The Law of Areas	187
15.7.	Orbits and Energy	189

19.	Temperature	191
19.1.	Thermal Equilibrium	191
19.2.	Measuring Temperature	191
19.3.	Other Temperature Scales	192
19.4.	Thermal Expansion	193
19.5.	The Mercury Thermometer	195

20.	Heat and the First Law of Thermodynamics	197
20.1.	Heat	197
20.2.	Heat Capacity	197
20.3.	Heat of Transformation	198
20.4.	Work	199
20.4.1.	Adiabatic Processes	201
20.4.2.	Constant Volume Processes	201
20.4.3.	Cyclical Processes	202
20.4.4.	Free Expansion	202
20.5.	Transfer of Heat	202
20.5.1.	Conduction	202
20.5.2.	Convection	204
20.5.3.	Radiation	205

21.	The Kinetic Theory of Gases	207
21.1.	Avogadro constant	207
21.2.	The Ideal Gas	207
21.3.	Pressure and Temperature: A Molecular View	209
21.4.	Translational Kinetic Energy	212
21.5.	Mean Free Path	212
21.6.	Heat Capacity of Ideal Gas	215
21.6.1.	Molar Heat Capacity at Constant Volume	215
21.6.2.	Molar heat Capacity at Constant Pressure	216
21.7.	The Adiabatic Expansion of an Ideal Gas	217

22.	Entropy and the Second Law of Thermodynamics	220
22.1.	Second Law of Thermodynamics	220
22.2.	The Engine	220
22.3.	The refrigerator	221
22.3.	The Carnot Cycle	221

1.	UNITS

	Measurements of physical quantities take place by means of a comparison with a standard.  For example: a meter stick, a weight of 1 kilogram, etc.

The  that will be used in this course are:

	 (m):	One meter is equal to the path length traveled by light in vacuum during a time interval of 1/299,792,458 of a second. 

	 (kg):	One kilogram is the mass of a Platinum-Iridium cylinder kept at the International Bureau of Weights and Measures in Paris. 

	 (s):	One second is the time occupied by 919,263,170 vibrations of the light (of a specified wavelength) emitted by a Cesium-133 atom. 

A unit that is being used as a base unit must be both accessible and invariable.  The original meter bar kept in Paris was not very accessible (this is still true for the kilogram).  In addition, the length of the standard bar is temperature dependent.  The definition of the meter in terms of the number of wavelengths of a particular atomic transition in Krypton-86 made the meter more accessible; the transition is characteristic for Krypton-86, and is the same for each Krypton-86 atom.  However,  Doppler shifts due to the thermal motion of the atoms can slightly change the wavelength, and produce a small uncertainty in the definition of the meter.  The current definition of the meter in terms of the speed of light is not affected by thermal motion: the speed of light in vacuum is constant, independent of temperature and velocity of observer and/or source.

	Example:  how to measure the distance d from the earth to the moon ?
	APOLLO astronauts placed a mirror on the moon.  It can be used to measure the distance between the earth and the moon very accurately.  The reflection of a laser beam aimed at this mirror reaches the earth after 2.495 s.  The distance can then be calculated:

	The definition of the standard mass makes it very inaccessible.  In principle, the weight of individual nuclei can be used as a standard; nuclear weight does not depend on location, temperature, pressure, etc.  However, counting the number of nuclei in a standard (or assembling a fixed number of nuclei) is an almost impossible task.

Note:

1.	Improved definitions of base units must be defined such that it matches the previous definition as closely as possible (no need to change all meter sticks in 1983).

2.	Speed of light is now defined as 299,792,458 m/s.

All physical quantities are expressed in terms of .  For example, the velocity is usually given in units of m/s.  All other units are  and may be expressed as a combination of base units.  For example (see Appendix A):

Other examples are:	density:  kg/m^3
	area:  m^2

^When ^dealing ^with ^very ^small ^or ^large ^numbers, ^it ^is ^convenient ^to ^use ^prefixes ^(see ^Table ^1.1, ^and ^Table ^1-2 ^on ^page ^3 ^in ^Halliday, ^Resnick, ^and ^Walker).
Factor | Prefix | Symbol
10^18 | exa- | E
10^15 | peta- | P
10^12 | tera | T
10^9 | giga- | G
10^6 | mega- | M
10^3 | kilo- | k
10^-3 | milli- | m
10^-6 | micro- | μ
10^-9 | nano- | n
10^-12 | pico- | p
10^-15 | femto- | f
10^-18 | atto- | a

Table 1.1.  SI Prefixes

Example:	2.35 10^-9 s  =  2.35 ns

In many cases, the data are not supplied in the correct units, and one needs to convert units (see Appendix F in Halliday, Resnick, and Walker).

Examples:	1”  =  2.54 x 10^-2 m
	55 miles  =  88 x 10^3 m
	1 h  =  3600 s
	55 miles/h  =  88 x 10^3/3600 m/s  =  24.4 m/s