Angular Momentum

Discussion

the idea

text

L =  r × p = r × m v
L =  m r × (ω × r) = m ω(r · r) − mr(r · ω) = mr2 ω − 0 = mr2 ω
L =  I ω

Moment of inertia again

I = ∑ r2m = ⌠
⌡		  r2 dm = ρ ⌠
⌡		  r2 dV

Conservation of angular momentum

∑ τ =  d  L = 0
dt

Thus

L = constant

concept translation connection rotation
momentum p = 
 m v L =  r × p = m r × v L =  I ω
impulse-momentum ∫ F · dt
F =
  = Δp
dp/dt
     ∫ τ · dt
τ = 
  = ΔL 
dL/dt
Translational and rotational quantities compared

spaceports

spaceports

location status name
australia disused Woomera Launch Site
australia proposed Cape York Spaceport
australia proposed Christmas Island Spaceport
china active 酒泉卫星发射中心 (Jiuquan Satellite Launch Center)
china active 太原卫星发射中心 (Taiyuan Satellite Launch Center)
china active 西昌卫星发射中心 (Xichang Satellite Launch Center)
china proposed 文昌卫星发射中心 (Wenchang Satellite Launch Center)
eu active Centre Spatial Guyanais (Guiana Space Center)
eu disused Hammaguir Launch Site
eu disused San Marco Equatorial Range
india active सतीश धवन अंतरिक्ष केंद्र (Satish Dhawan Space Centre)
iran active Semnan Space Satellite Launch Center
israel active Palmachim Air Force Base
japan active 種子島宇宙センタ (Tanegashima Space Center)
japan active 内之浦宇宙空間観測所 (Uchinoura Space Center)
korea, s active 나로우주센터 (Naro Space Center)
mexico proposed Agencia Espacial Mexicana (Mexican Space Agency)
russia active Космодром Байконур (Baikonur Cosmodrome)
russia active Космодром Капустин Яр (Kapustin Bluff Cosmodrome)
russia active Космодром Плесецк (Plesetsk Cosmodrome)
russia active Космодром Свободный (Freedom Cosmodrome)
russia active Пусковая База «Ясный» ("Yasniy" Launch Base)
us active Kennedy Space Center
us active Vandenberg Air Force Base
us active Wallops Flight Facility
us active Kodiak Launch Complex
us active Ronald Reagan Ballistic Missile Defense Test Site
us active Sea Launch
Orbital spaceports

the earth

The earth is not the world's best clock.


[magnify]


[magnify]

types of LOD change … horrible mess …

  1. a linear increase owing to tidal dissipation. Paraphrase, "The tidal friction between the oceans and the Earth's surface causes the Earth's rotation to slow by approximately 0.002 seconds every century. However, ignoring energy lost to heat generated by the tides, the angular momentum of the Earth-Moon system must remain constant. The Earth's angular momentum is decreasing, so the Moon's must increase. The only way it can do this is by moving into a higher orbit around the Earth. Thus, the distance to the farthest point of the lunar orbit is increasing by about 3.8 centimeters per year."
  2. Larger, irregular variations, on the scale of decades, owing to core-mantle interactions
  3. Solar flares are known to abruptly alter the Earth's rotation. For example, the great flares of 1959 and 1972 brought abrupt changes in the LOD. Both long-term and short-term changes in solar activity alter the Earth's rotation. The 11-year, 22-year and 56-year solar cycles are conspicuous in the LOD data. Long-term (secular) changes were noted at times of fluctuations in solar activity in the past, and the evidence indicates that these changes were very likely abrupt. Observations of the LOD, like so many other geophysical phenomena, reveal the solar-FEM linkage.
  4. Seasonal changes from the angular momentum exchange between crust and atmosphere.

The rate of rotation of the earth is high in summer and low in winter (northern hemisphere).

At time scales of hours to days, tidally driven? ocean currents and variations in the ocean height dominate

 
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