Lecture 1

Review of Phys 101

UNITS : we will mostly use the standard units m(eter), k(ilo)g(ram) and s(econd) - and the ones derived from them - but we must be comfortable in converting from these to any other known unit

Helpful rule : "dimension matching"

Example : how many centimeters in 10 inches ? Need to know "conversion factor":

2.54 cm/inch

10 in = 10 in $\times$ 2.54 cm/in = 25.4 cm

Knowing the conversion factor, we can easily do the opposite conversion :

2.54 cm/in $\longrightarrow$ 1/2.54 in/cm.
Therefore, if we want to know,e.g., how many inches in 50 cm:

50 cm = 50 cm $\times$ 1/2.54 in/cm = 19.7 in

MULTIPLES and SUBMULTIPLES

10 10¹ deca 1/10 10^-1 deci

100 10² hecto 1/100 10^-2 centi

1000 10³ kilo 1/1000 10^-3 milli

1000,000 10⁶ Mega 1/1000,000 10^-6 micro

10⁹ Giga 10^-9 nano

10¹² Tera 10^-12 pico

10¹⁵ Peta 10^-15 femto

SCIENTIFIC NOTATION.

Throughout the course, our explorations will range from the smaller possible objects (quarks?neutrinos?) to the largest dimension of the universe. It will be useful to represent numbers in the "scientific notation". Any number x can be written in the form :

$x = y\times 10^{n},$

n >,< or = 0 (remember : x⁰=1)

Examples :
$123456789 = 1.23456789\times 10^{8},$
$0.0000002 = 2\times 10^{-7}$

MULTIPLICATION : $(x\times 10^{n})\times (y\times 10^{m}) = x\times y \times 10^{n+m}$


DIVISION : $(x\times 10^{n})/(y\times 10^{m}) = x/y \times 10^{n-m}$

Examples :
How many seconds in a year ?


















How many grains of sand (one grain = 5 mg) in a 20 kg sandpile?

Enough with Mathematics, let's come back to Physics, and review some of the most important quantities/concepts.

VELOCITY (vector) and SPEED (scalar: speed = magnitude of vector velocity) :
[0.1in] distance covered in unit time, velocity = distance/time, i.e. :

v = d/t, d = vt, t = d/v

(Note : above expressions refer to constant -or at least average- velocity)


ACCELERATION : rate of change of velocity.
Units : [(meters per sec) per sec], m/s²

a = (v_f-v_i)/t

INTERESTING CASE OF MOTION : Uniform Circular Motion, constant speed, variable velocity, therefore there must be an acceleration (which turns out to be a = v²/r)

NEWTON'S (SECOND) LAW OF MOTION :

$\overline{F} = m\overline{a}$

Special case : $F = 0\longleftrightarrow a = 0\longleftrightarrow v = const$
[0.5in] NEWTON'S LAW OF UNIVERSAL GRAVITATION :

all massive objects attract each other according to:

$F = G\times\frac{m_{1}m_{2}}{d^{2}}$

$G= 6.67 \times 10^{-11} Nm^{2}/kg^{2}$


Motion of planets, satellites, etc. is governed by Law of Gravitation

ENERGY

Energy is one of the most fundamental concepts in Physics (and Science in general). Probably it will be intervene in all of the coming lectures. In spite of its importance, it is not an easy quantity to define.

Definition from Mechanics : Energy is the ability to do Work

Definition of Work:

W(ork) = F(orce)$\times$d(isplacement)

In order to do Work, Energy must be spent. More importantly: Energy can exist in many different forms:

KINETIC (energy due to motion) :

body in motion
thermal energy (heat)
energy carried by waves

POTENTIAL:

Elastic
Gravitational
ElectroMagnetic
Chemical (electromagnetic)
Nuclear

Energy can (and does) transform from one form to another, but TOTAL ENERGY IS CONSERVED (but note : even though Energy Conservation is one of the most important concept in Physics, it is an assumption, not a proven Law).

POWER (measured in watts): rate of doing Work (or of consuming Energy),

P(watts) = W(joules) / t
P(watts) = E(joules) / t

HEAT TRANSFER can occurr via

CONDUCTION (solids and fluids)
CONVECTION (fluids)
RADIATION (even in vacuum)

2^nd LAW of THERMODYNAMICS:

Heat migration: hot $\rightarrow$cold,
Order$\rightarrow$Disorder,
Less Probable$\rightarrow$More Probable

ELECTROMAGNETISM

Electrostatic attraction (unlike charges, +-) or repulsion (like charges, ++,- ) governed by Coulomb's Law:

$F = k\times\frac{q_{1}q_{2}}{d^{2}}$

Relative strength of electrical vs. gravitational forces (pages 173,174):
electricity/gravity = 2.6$\times$10³⁹, an enormous number !!


Basic facts of life concerning Electricity and Magnetism :

Moving charges (electric currents) generate magnetic fields

Moving magnets (variable magnetic fields) put charges in motion (generate electric currents)

ElectroMagnetic Fields affect motion of charged particles

WAVES are characterized by

Wavelength $\lambda$
Frequency $\nu$
Velocity of propagation v
Amplitude A

v = $\lambda\nu$

Waves can exhibit phenomena of Interference (Constructive or Destructive)


Electricity and Magnetism are just to aspects of the same underlying phenomenon. Maxwell's equations predict the existence of ElectroMagnetic Waves, that must propagate at the speed of light $\longrightarrow$ Spectrum of EM waves.