M5 Advanced Mechanics Flashcards
Projectile motion
a(x) = 0 v(x) = ucos(theta) x = utcos(theta) a(y) = -g v(y) = -gt + usin(theta) y = -gt2 / 2+utsin(theta)
Pendulum
T = 2pi x sqrt(L/g)
Centripetal force
towards the centre Fc = mv2/r formula sheet.
Centrifugal force
reaction force to centripetal force.
Tangential velocity
v = 2r x pi / T
Angular displacement
change in theta = s/r where s is length round the circumference, r is radius and theta is in radians.
Angular velocity
w = change in theta / change in time wr = v where r is radius, v is linear/tangential velocity
Conical Pendulums
Fc = T + mg
Newton’s Universal Law of Gravitation
F = GMm/r2 r measured from centre of masses
Gravitational Field Strength
F per unit mass g = Gm/r2
Kepler’s Three Laws of Planetary Motion
- The planets move in ellipses with the sun at one focus.
- The line between the Sun and the planet sweeps out equal areas in equal time.
- T2 is proportional to r3. r3/T2 = GM/4pi2
Escape velocity
let change in U = EK
v = sqrt(2GM/r)
Orbital Velocity
let Fg = Fc v = sqrt(GM/r)
Geostationary Orbit
- stays in the same place relative to the earth, T = 1 day
- Above outer Van Allen, 35 000km
- wide field of view
- allows tracking of stationary point on Earth
- used for communications, mass-media, weather monitoring
Low Earth Orbit
- 160 to 2000 km (below inner Van Allen belt)
- small field of view
- frequent coverage of specific or varied locations
- difficult to maintain orbit due to satellite drag
- used for military, earth observation, shuttle missions, Hubble space telescope
Polar Orbit
- period can be as low as 30 minutes
- orbits around the poles, almost perpendicular to the equator
- used for weather, climate, oceans, volcanoes and vegetation patterns
Potential energy of a planet/satellite in orbit
U = -GMm/r
negative as U approaches 0 as r approaches infinity
Kinetic energy of a planet/satellite in orbit
EK = mv2/2 where v2 = GM/r EK = GMm/2r
Total energy of a planet/satellite in orbit
U + EK = -GMm/2r
