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Gravitation

Gravitation. Gravitational Force. the mutual force of attraction between particles of matter Newton’s Law of Universal Gravitation F g =G(m 1* m 2 /r 2 ) G= 6.67x10 -11 Nm/kg2. Force. Force is proportional to the mass times mass

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Gravitation

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  1. Gravitation

  2. Gravitational Force • the mutual force of attraction between particles of matter • Newton’s Law of Universal Gravitation • Fg=G(m1*m2/r2) • G= 6.67x10-11 Nm/kg2

  3. Force • Force is proportional to the mass times mass • Force is inversely proportional to the distance squared or the radius squared

  4. Elliptical Orbits • http://spaceweather.com/swpod2007/23oct07/orbit.gif

  5. Elliptical orbits • Perigee greatest force • greatest velocity • smallest distance

  6. Elliptical orbits • Apogee least force • least velocity • greatest distance

  7. Circular orbits • distance is constant • velocity is constant • Fc is constant

  8. Kepler’s Laws • First Law Each planet travels in an elliptical orbit around the sun with the sun as one focal point • Second Law- An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. • Third Law- The square of an orbital’s period is proportional to the cube of the average distance between the planet and the sun T2 is proportional to t3

  9. Equations • T=2π√(r3/Gm) • v=√(Gm/r)

  10. Circular Motion • = the movement of an object at constant speed around a circle with fixed radius • Axis – straight line around which rotation takes place • Rotation – object turns around an internal axis • Ex. Ice skater • Revolution – object turns around an external axis • Ex. Earth around the sun

  11. Rotational Speed • Linear speed – distance/time • Tangential speed – speed along a circular path • Rotational speed – number of rotations per unit of time • Example: Carousel horses travel at same rotational speed but different tangential speed

  12. Centripetal Force • Force that causes an object to follow a circular path • Ex. Force holding occupants safely in a rotating carnival ride • Fnet = mv2 r

  13. Centripetal Acceleration • Always points toward the center of the circular motion. • Period (T) = time needed for an object to make one complete revolution • Distance traveled = circumference • Circumference = 2πr = πd

  14. Other formulas • Centripetal Acceleration equals the velocity squared divided by the radius • Ac = v2/r • The number of revolutions equals the distance traveled divided by the circumference • Revolutions = distance/circumference

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