8 01 31

G-k-M-k-G _A_ one $\omega_0$
G-k-m-k-m-k-G _A_A_ two $\omega_0$
G-k-m-k-m-k-m-k-G [<- connection diagram] _A_A_A_ [<- spectrum diagram 'A' is peak]
continuum G-T/\mu-G _A_ 1st -A-V- 2nd -A-V-A- 3rd
"normal frequencies" "natural frequencies"
!$\sigma$coupling-bond single-saturated-series coupling

Lec 31 | 8.01 Physics I: Classical Mechanics, Fall 19994

8 02 19

"atrium" "ventricle"
heart cell (10um) inside -80mV -depolarization-> +20 relative to surface and contract in 0.2S
electric dipole formation same field direction both way but pulsive 0.2S apart.$V = \integral E \cdot dl$
2 - 3 milliVolt between standard 12 electrodes P R T U can be 3 = 2 on arms and on a leg.
"Other muscle cells generate E field also"
this year is 50 years low in sun activity. "magnetic pressure" $[N/m^2]$ $P = \frac{B^2}{2 \mu_0}$

Lec 19 | MIT 8.02 Electricity and Magnetism, Spring 2002

8 02 31

半径を角度で表すのは実はナチュラル　sun in the sky $0.5^\circ (30^{\hat\circ}) proceeds 15^\circ / hour (30 suns / hour)$
super numerical bow "proof" of a saint

Lec 31 | MIT 8.02 Electricity and Magnetism, Spring 2002

8 03 21

$\theta$ real angle visible, $\delta$ phase angle not visible
! RGB CMY diagonal relationship $1^{st}, 2^{nd} 0^{th}$
pupil diameter 3mm $\perpto$ large D -> 'capital' D
smaller the opening the broader the image
$/$ ... 'divided by' "single slot diffraction and multiple-slot interference the same thing"
$\times 1.22$ for circular opening $90^{\hat\prime}$

Lec 21 | MIT 8.03 Vibrations and Waves, Fall 2004

私だけが知っているスゴいウェブページ

Texが好きでLaTeXMathMLを使っていたけど、つい最近まで
A Brief Introduction to LaTeXMathML
が全部TeXで書かれたウェブページだとは気がつかなかった。
スゲー！！

8 03 20

#lights go through two opening at fixed phase relationship
same sum -> ellipse, same difference in lengths -> hyperbola
r reflectivity ... amplitude ratio $r = \frac{n_1 - n_2}{n_1 + n_2}$
fringe

Lec 20 | MIT 8.03 Vibrations and Waves, Fall 2004

8 02 30

"HN50 polarizer(polarimeter)" ideal
Malus' Law $\frac{1}{2}I_0 \cos^2\theta$
$\parallel$
偏光で遠方から視覚的に金属かそうでないかが区別できる。
形、色、偏光方向。音で同じ物理量はないだろうか

Lec 30 | MIT 8.02 Electricity and Magnetism, Spring 2002

8 01 30

鉛筆に加え、左手の指特に人差し指を使ってみる。
$[ \tau ] = [ N m ] = [ 'work' ]$

Lec 30 | 8.01 Physics I: Classical Mechanics, Fall 1999

8 03 23

Lec 23 | MIT 8.03 Vibrations and Waves, Fall 2004

$\tau = I \ddot\theta$
$360^\circ \approx 365.25 (days/year) $
$ 3 10^8 \def 'light second'$

8 02 29

$90^\degr 90^\circ$ $RGB -> RGV$

Lec 29 | MIT 8.02 Electricity and Magnetism, Spring 2002

8 01 29

Lec 29 | 8.01 Physics I: Classical Mechanics, Fall 1999
"Newton's cradle" pulley "Atwood Machine"
$v ,v^\prime$ $\alpha = \dot{\omega} = \ddot\theta$

8 01 28

Lec 28 | 8.01 Physics I: Classical Mechanics, Fall 1999
Archimedes' Principle:  not Volume versus density but two weight one in air and the other in water.
And Buoyant force is the weight($'mass' \times 'g'$) of the displaced fluid by immersed body.
"capsize"
Bernoulli: conservation of energy per unit volume$\frac{1}{2}\rho v^2 + \rho g y + Pressure@y = C$
Pressure is Potential per unit Volume.

8 02 27

Lec 27 | MIT 8.02 Electricity and Magnetism, Spring 2002
$\lambda = \frac{2 \pi}{k}$
$T = \frac{2 \pi}{\omega}$
E & B propagation through vacuum
E & B are 'potentials'  $F = q E ; \vec{F} = q \vec{v}\times\vec{B}$

8 01 27

Lec 27 | 8.01 Physics I: Classical Mechanics, Fall 1999

"Pascal's principle comes" from  "Pressure is scaler"
"liquid practically incompressible" $atmospheric pressure 1 kg / cm^2, Hg 760mm H_2 O 10m$
"empty MT" "AT atmosphere"

8 03 22

sun 1/2 degree
rainbows 2,3 degrees
$sunglasses \perp rainbow$
"sun dogs?" "glory"
D for Dots & Defraction
$42.{\degree}89$

Lec 22 | MIT 8.03 Vibrations and Waves, Fall 2004

8 01 26

Lec 26 | 8.01 Physics I: Classical Mechanics, Fall 1999

'stress' = Young 'strain' $ \frac{F}{A} = Y \frac{\Delta l}{l}
若者がありあまる体力・気力にまかせて無理すると(本人にとっても回りの'老人'にも)ストレスとなる。
Young率が高いほどお硬い。
でも未だ素直("linear")。いずれダラダラになって"plastic flow" -> "break down"
tensile force compressive force

8 02 26

$ k = 2 \pi / \lambda $
$ T = 2 \pi / \omega $
は
$ T = 1 / f $はすぐ分かる関係で$\omega$は$f$の$2\pi$版だと思えば$ T = 2 \pi / \omega $は形式的に分かる。分子と分母に分かれているのは$\omega$の'radian作用'を打ち消す感覚。
$ k = 2 \pi / \lambda $は$\lambda = 2 \pi / k$つまり$k$は'空間周波数'$1 / \lambda$の'radian版'。
'空間周波数'に名前・シンボルがないのがイタい。'時間周波数$T$'に対して形が似ている$Y$を考えれば$\lambda$をひっくり返した形さらに空間'X,Y,Z'と連想しやすいかも。
$ T \omega = 2 \pi$(ティーオメガ)と$ k \lambda = 2 \pi$(ケーラムダ)と音で覚え$f$は忘れる。音で覚えるといえば$v = \sqrt{\frac{T}{\mu}}$ $v = \sqrt{\frac{Temp}{M}}$ $v = \sqrt{\frac{k}{m}}$ $v = \sqrt{\frac{g}{m}}$といった一連の$v$に関する公式がある。

Lec 26 | MIT 8.02 Electricity and Magnetism, Spring 2002

8 01 25

$\tan = \sin \over \cos$
$\sin = sin \over 1$
$\cot = \cos \over \sin$
$\frac{T_2}{T_1} = e^{\mu \theta_0}$
$\vec\tau_P = \vec{r_P} \times \vec{F} = I_p \vec\alpha$
use static equilibrium to determine 'center of mass' experimentally

Lec25 | 8.01 Physics I: Classical Mechanics, Fall 1999

8 02 24

"pure roll" $V_Q == V_{circ}$
"precession"
$L = I \omega$
$\tau = I \alpha$

Lec 24 | 8.01 Physics I: Classical Mechanics, Fall 1999

8 02 25

1/2 = \int_{one-cycle} cos^2 \theta d \theta ... "time averaged cos squared"
L \def \phi /over I.  Ferro magnetic material increase \phi while I is kept constant. -> L goes  up by definition.

Lec 25 | MIT 8.02 Electricity and Magnetism, Spring 2002

Lamor formula

The Lamor formula
Walter Lewinの講座にあった加速度と電荷とパワーの関係

8 01 23

one \over frequency
half the stars are binary

Lec 23 | 8.01 Physics I: Classical Mechanics, Fall 1999