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 = | m v | L = | r × p = m r × v | L = | I ω |
| impulse-momentum | ∫ F ⋅ dt = F = |
∆p dp/dt |
∫ τ ⋅ dt = τ = |
∆L dL/dt |
||
spaceports
spaceports
| country | status | name |
|---|---|---|
| au | disused | Woomera Launch Site |
| au | canceled | Cape York Spaceport |
| au | proposed | Christmas Island Spaceport |
| br | active | Alcantara Launch Center (Centro de Lançamento de Alcântara) |
| cn | active | Jiuquan Satellite Launch Center (酒泉卫星发射中心) |
| cn | active | Taiyuan Satellite Launch Center (太原卫星发射中心) |
| cn | active | Wenchang Satellite Launch Center (文昌卫星发射中心) |
| cn | active | Xichang Satellite Launch Center (西昌卫星发射中心) |
| fr | active | Guiana Space Center (Centre Spatial Guyanais) |
| fr | disused | Hammaguir Launch Site |
| it | disused | Luigi Broglio Space Centre |
| in | active | Satish Dhawan Space Centre (सतीश धवन अंतरिक्ष केंद्र) |
| in | active | Vikram Sarabhai Space Center (विक्रम साराभाई अंतरिक्ष केंद्) |
| ir | active | Imam Khomeini Space Center |
| il | active | Palmachim Air Force Base (בָּסִיס חֵיל-הַאֲוִויר פַּלְמַחִים) |
| jp | active | Tanegashima Space Center |
| jp | active | Uchinoura Space Center (内之浦宇宙空間観測所) |
| kp | active | Tonghae Satellite Launching Ground (동해위성발사장) |
| kp | active | Sŏhae Satellite Launching Station (서해위성발사장) |
| kr | active | Naro Space Center (나로우주센터) |
| mx | proposed | Mexican Space Agency (Agencia Espacial Mexicana) |
| nz | active | Mahia Launch Complex |
| ru | active | Baikonur Cosmodrome (Космодром Байконур) |
| ru | active | Vostochny Cosmodrome (Космодром Восточный) |
| ru | active | Kapustin Yar Cosmodrome (Космодром Капустин Яр) |
| ru | active | Plesetsk Cosmodrome (Космодром Плесецк) |
| ru | active | Yasniy Launch Base (Пусковая База Ясный) |
| ru | disused | Svobodniy Cosmodrome (Космодром Свободный) |
| 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