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Episode 19
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20:30
Angular Momentum
start of goodstein
Kepler-II - vortices of hurricanes, bathtubs law of conservation of angular momentum
renaissance - Christian theology - Reformation/counter-Reformation - bloody 30yrs-war - 3 giants on earth - Galileo, Kepler, Brahe
Kepler 1571-1630 - ups and downs - wife fat confused simpleminded - wrote
about his feelings with his science - today: flawless;
professional astrologer - to make ends meet - a genius - shape of winebarrels,
almost invented calculus - 3 laws correct
K-II - explains shape of galaxies, fury of hurricanes, whirlpools - law of
conservation of angular momentum
Kepler stood up to the classical astronomers of 2000yrs of collective wisdom.
Astronomy was the first physical science - ancient China, Greece, Alexandria,
Babylon, Mayans, Baghdad - heaven on earth - Greeks created original schemes Aristotle - nature of everything under the sun - earth is the center of the universe heavenly bodies move along circles - complicated circles moving on top of
complicated circles - epicycles, complex, almost uncomprehensible - “save the
appearances” - more or less predicted positions of stars and planets, aided
navigation, cast horoscopes. Earth @ center, motion circular
Copernicus 1500 wrote “revolution of heavenly orbs” - earth hurtling thru space Sun @ center - earth a mere planet in orbit around sun - revolutionary idea revolution meant radical change since then - not perfect circles; epicycles still
required, revolution almost hidden behind astronomical complexity. Kepler
inspired by this, eschewed circular motion.
Kepler the wandering mathematician
K-I, K-II, III
water down the drain - forms a vortex, hurricane
Kepler’s description, not explanation
K-II - equal areas - r, r, r + r - cross product – PHYSICS 115 DON’T WORRY
ABOUT THIS DERIVATION - area of triangle is ½r (r + r) = ½r r, so A/t
[Phys 115] (=dA/dt [Phys 201]) = ½ r  v
ice skater - conservation of angular momentum
ordinary momentum - F=dp/dt =p/t
angular momentum F, r, the twist - r  F - twist needed to get something going but in orbit there’s no twist, or in vortices - r  F = 0
F=0 -> p=const., correspondingly r  F = 0 -> L=const. Differentiating don’t
worry L = mr  v; dL/dt = r  F =  (torque) - angular momentum conserved in
orbit that’s why K-II.
spinning body keeps spinning
L = mr  v - vector, magnitude mrv if r  v [e.g. circle]
constant - so if r down, v up
no viscosity - whirlpool red spot - hurricane since at least 1610. - galaxies, flat disk about globular center angular momentum helps to design the universe
22:00 back to Goodstein - 1562 major conjunction of planets - Copernican tables were
even worse than old method - Tycho Brahe - 1546-1601 - b/c continuous precise
observations were not done; so he did it - created Tychonic universe
Aristotle: earth ctr
Copernicus - sun ctr
Tycho - earth ctr, sun around earth, other planets around sun – compromise crystal spheres smashed - “we know” his most important accomplishment was
careful systematic observations went from 10' of arc uncertainty to 2' of arc crucial improvement
25:30 end of Goodstein
angular momentum is r  v
Force applying twist is torque is r  F
 = rate of change of angular momentum - no torque, L conserved
26:00 end
Episode 20
Torques & Gyroscopes
32:00
35:15
Goodstein—conservation & Newton’s laws
transportation—the wheel invented by Sumerians
spinning wheel animation
torque=r x F
what keeps a wheel from falling? Animation
precession—top animation
gyroscope
navigation & gyroscopes
polar routes, space
precession—wheel & top animation, derivation
earth as a gyroscope (the only ‘perfect’ gyroscope)
equinoxes, equinox drift
polaris’ drift
Copernicus first to explain drift—precession
Newton—torque acts on bulge of earth; axis precesses very slowly
Goodstein
45:21
46:50
49:59
54:51
56:10