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Circular Motion

Circular Motion. Centripetal Force Apparent Weight Newtons’ Universal Gravitation Law. Centripetal accel. & Force. v = 2 p r/T a cp = v 2 /r F cp = mv 2 /r Centripetal = center seeking. a cp & F cp are both toward the central body.

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Circular Motion

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  1. Circular Motion Centripetal Force Apparent Weight Newtons’ Universal Gravitation Law

  2. Centripetal accel. & Force • v = 2pr/T • acp = v2/r • Fcp = mv2/r • Centripetal = center seeking. acp & Fcp are both toward the central body. • Fcp is the force exerted by the central body on the orbiting body. (Recall Newton’s 3rd) • acp is the accel. of the orbiting body caused by that force. • Direction of v?

  3. Centrifugal • p. 156 text - “A Nonexistent Force” • This is not really true - just misused. • Centrifugal = center fleeing • Force exerted by orbiting body on the central body • Newton’s 3rd - axn/rxn forces

  4. Apparent Weight • What the weight of an object appears to be as a result of the acceleration of a supporting. • Faw = m(g-a) • Ex. of supporting bodies - elevators & space stations & rockets - oh my! • When an orbiting body is accel. @ a rate of g weightlessness occurs.

  5. Newton’s Universal Law of Gravitation • Fg = Gm1m2/r2 • For earth: Fg = GMem/r2 • Fg is also wt. therefore, mg = GMem/r2 • mg = GMem/r2 • g = GMe/r2 • What does this tell us?

  6. Usefulness of Newt’s Univ. Grav. Law. • Observation Fcp ≠ one of the fundamental forces • Sometimes Fcp = Fg • Knowing when is the key! • If mass is the cause of the force then Fcp = Fg • Therefore, mv2/r = GMem/r2 • mv2/r = GMem/r2 • v2/r = GMe/r2 & v2 = GMe/rthus v = GMe/r

  7. Usefulness of Newt’s Univ. Grav. Law. • But v = 2pr/T • So 2pr/T = GMe/r • thus4p2r2/T2 = GMe/r • and 4p2r3/T2 = Gme so 4p2r3 = GMeT2 • T2 = 4p2r3/Gme • T = 2p r3/Gme

  8. Usefulness of Newt’s Univ. Grav. Law. • Therefore, we can determine all sorts of information about central & orbiting bodies if we know other information. • This is how they know the mass of the sun & planets & moons etc.

  9. Kepler’s 3rd Law • T2/R3 = k • Applies to any given orbited or central body.

  10. Newt’s Univ. Gav. Law & Kepler’s 3rd Law. • 4p2r3/T2 = Gme • Since4p2 & Gme areall constant • r3/T2 or T2/r3 = k which is Kepler’s 3rd law. • Although Kepler (1571-1630) preceded Newton (1643-1727). Kepler’s 3rd Law follows from Newton’s Universal Law of Gravitation.

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