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
| concept | translation | connection | rotation | |||
|---|---|---|---|---|---|---|
| momentum | p = | mv | L = | r × p = mr × v | L = | Iω |
| impulse-momentum | ∫ F · dt F = |
= ∆p dp/dt |
∫ τ · dt τ = |
= ∆L dL/dt |
||
spaceports
spaceports
| location | status | name |
|---|---|---|
| australia | disused | Woomera Launch Site |
| australia | proposed | Cape York Spaceport |
| australia | proposed | Christmas Island Spaceport |
| brazil | active | Centro de Lançamento de Alcântara (Alcantara Launch Center) |
| 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 | 文昌卫星发射中心 (Wenchang Satellite Launch Center) |
| china | active | 西昌卫星发射中心 (Xichang 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 | پایانه فضایی امام خمینی (Imam Khomeini Space 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, n | active | 동해위성발사장 (East Sea Satellite Launch Site) |
| korea, n | active | 서해위성발사장 (West Sea Satellite Launch Site) |
| korea, s | active | 나로우주센터 (Naro Space Center) |
| mexico | proposed | Agencia Espacial Mexicana (Mexican Space Agency) |
| nz | active | Mahia Launch Complex |
| russia | active | Космодром Байконур (Baikonur Spaceport) |
| russia | active | Космодром Восточный (Eastern Spaceport) |
| russia | active | Космодром Капустин Яр (Kapustin Bluff Spaceport) |
| russia | active | Космодром Плесецк (Plesetsk Spaceport) |
| russia | active | Пусковая База Ясный (Yasniy Launch Base) |
| russia | disused | Космодром Свободный (Freedom Spaceport) |
| 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 |
the earth
The earth is not the world's best clock.
types of LOD change … horrible mess …
- 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."
- Larger, irregular variations, on the scale of decades, owing to core-mantle interactions
- 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.
- 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