Angular Momentum

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Angular Momentum

Discussion

the idea

text

L =r × p
L =r × mv
L =mr × (ω × r)
L =mω(r · r) − mr(r · ω)
L =mr2ω − 0
L =mr2ω
L =Iω

Moment of inertia again

I = ∑ r2m = 
r2 dm = ρ
r2 dV

Conservation of angular momentum

∑ τ =d L = 0
dt

Thus

L = constant

Translational and rotational quantities compared
concepttranslationconnectionrotation
momentump =mvL =r × p = mr × vL =Iω
impulse-momentum∫ F · dt
F =
 = Δp
dp/dt
∫ τ · dt
τ =
 = ΔL
dL/dt

spaceports

spaceports

locationstatusname
australiadisusedWoomera Launch Site
australiaproposedCape York Spaceport
australiaproposedChristmas Island Spaceport
chinaactive酒泉卫星发射中心 (Jiuquan Satellite Launch Center)
chinaactive太原卫星发射中心 (Taiyuan Satellite Launch Center)
chinaactive西昌卫星发射中心 (Xichang Satellite Launch Center)
chinaproposed文昌卫星发射中心 (Wenchang Satellite Launch Center)
euactiveCentre Spatial Guyanais (Guiana Space Center)
eudisusedHammaguir Launch Site
eudisusedSan Marco Equatorial Range
indiaactiveसतीश धवन अंतरिक्ष केंद्र (Satish Dhawan Space Centre)
iranactiveSemnan Space Satellite Launch Center
israelactivePalmachim Air Force Base
japanactive種子島宇宙センタ (Tanegashima Space Center)
japanactive内之浦宇宙空間観測所 (Uchinoura Space Center)
korea, sactive나로우주센터 (Naro Space Center)
mexicoproposedAgencia Espacial Mexicana (Mexican Space Agency)
nzproposedRocket Lab
russiaactiveКосмодром Байконур (Baikonur Spaceport)
russiaproposedКосмодром Восточный (Eastern Spaceport)
russiaactiveКосмодром Капустин Яр (Kapustin Bluff Spaceport)
russiaactiveКосмодром Плесецк (Plesetsk Spaceport)
russiadisusedКосмодром Свободный (Freedom Spaceport)
russiaactiveПусковая База Ясный (Yasniy Launch Base)
usactiveKennedy Space Center
usactiveVandenberg Air Force Base
usactiveWallops Flight Facility
usactiveKodiak Launch Complex
usactiveRonald Reagan Ballistic Missile Defense Test Site
usactiveSea Launch
Orbital spaceports

the earth

The earth is not the world’s best clock.

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).

  • exchange of angular momentum between the solid Earth and the atmosphere
  • yearly melting of snow and ice in northern Spring
  • and distribution of groundwater?

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

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