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Dynamics

Dynamics. Dynamics Rotational K.E. Tides g as a function of latitude. Part IV – “ If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent. ”. Revision: READ the Textbook! Do the past papers – ideally under exam like conditions.

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Dynamics

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  1. Dynamics Dynamics Rotational K.E. Tides g as a function of latitude Part IV –“If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent.” Revision: READ the Textbook! Do the past papers – ideally under exam like conditions http://www.hep.manchester.ac.uk/u/parkes/Chris_Parkes/Teaching.html Chris Parkes October 2012

  2. Myth of Newton & apple. He realised gravity is universal same for planets and apples m2 m1 Gravitational Force • Any two masses m1,m2 attract each other with a gravitational force: F F r Newton’s law of Gravity Inverse square law 1/r2, r distance between masses The gravitational constant G = 6.67 x 10-11 Nm2/kg2 • Explains motion of planets, moons and tides mE=5.97x1024kg, RE=6378km Mass, radius of earth Gravity on earth’s surface Or Hence,

  3. N.B. general solution is an ellipse not a circle - planets travel in ellipses around sun Satellites • Centripetal Force provided by Gravity m R M Distance in one revolution s = 2R, in time period T, v=s/T T2R3 , Kepler’s 3rd Law • Special case of satellites – Geostationary orbit • Stay above same point on earth T=24 hours

  4. Comparable masses in orbit Masses m1,m2; Radii r1,r2 • Example Pluto (dwarf planet) and Charon (a moon) • mPluto = 1.31 x 1022 kg • orbit 6.39 days • r (mean) =19,600 km • Find mCharon/mPluto (11%) Photo Hubble Space Telescope

  5. Tides • Tides caused by difference in force exerted by moon on mass at near side and far side of Earth • Tides on both sides of Earth – given point two tides per day [Zooniverse] In middle of ocean variation in water level approx. 50 cm

  6. Neap tide / Spring tide • Sun attraction also has tidal effect • See Q4 week 12 question sheet • When moon and sun align – stronger – spring tide • When out of phase – weaker – neap tide • Occur twice per lunar month

  7. Apparent weight with latitude • At Equator require net force on body to keep in circular motion – hence apparent weight changes • Earth rotates on its axis – not an inertial frame Where ϕ is angle from equator plane

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