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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION. CIRCULAR MOTION. Uniform Circular Motion period, T : time for one complete revolution, unit: s speed is constant v = 2 p r/T (r: radius). velocity is constantly changing (because direction is changing). CIRCULAR MOTION.

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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  1. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

  2. CIRCULAR MOTION • Uniform Circular Motion • period, T: time for one complete revolution, unit: s • speed is constant • v = 2pr/T(r: radius) • velocity is constantly changing(because direction is changing)

  3. CIRCULAR MOTION • all turning objects have centripetal(center- seeking) acceleration

  4. CIRCULAR MOTION • centripetal acceleration, ac = v2/r • the greater the speed, the greater the centripetal acceleration • the smaller the radius of the turn, the greater the centripetal acceleration • a centripetal acceleration requires a centripetal force

  5. CIRCULAR MOTION • no centripetal force =no turning (linear motion)

  6. CIRCULAR MOTION • centripetal force, Fc = mv2/r any force can be a centripetal force: gravity (planets & moons), friction (car turning a corner), tension (ball on a string), etc.

  7. CIRCULAR MOTION • Frames of Reference - inside a turning object, there seems to be a centrifugal (center- fleeing) force pulling on objects

  8. CIRCULAR MOTION • Frames of Reference - outside the turning object, we see objects inside move in a straight line(inertia), until they get pulled into the turn by centripetalforce

  9. CIRCULAR MOTION • centrifugal force only exists within the turning object’s frame of reference - it is a fictitious force

  10. CIRCULAR MOTION • Frames of Reference - things moving on a rotating object seem to be made to turn by the “coriolis force”

  11. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

  12. QUIZ 3.1 A 50 kg child on a merry-go-round sits 2.0 m from the center and makes 2.0 complete revolution every second. (a) Find the child's period. (b) Find the child's tangential speed. (c) Find the child's centripetal acceleration. (d) Find the centripetal force on the child. v = 2pr/T ac = v2/r Fc = mv2/r

  13. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

  14. UNIVERSAL GRAVITATION • Newton's Law of Universal Gravitation: masses attract • gravity force is proportional to each mass • twice the mass = twice the force • gravity force is inversely proportional to the square of the distance between the masses • twice the distance = ¼ the force • distance measured from center of mass: point on a body around which mass is balanced

  15. UNIVERSAL GRAVITATION • Newton's Law of Universal Gravitation: • Fg = Gm1m2/r2 • FG: force of gravity, m: mass, r: distance between masses • G: universal gravitational constant, 6.67×10-11 Nm2/kg2 • gravity is only significant for very large masses

  16. UNIVERSAL GRAVITATION • acceleration due to gravity, g = Gme/r2 • Also known as the gravitational field strength • me: earth's mass (5.97×1024 kg) • r: distance from earth’s center (6.38×106 m + altitude) • g is only 9.80 m/s2 at sea level – it decreases as altitude increases • g is different on other planets & moons (it depends on the planet’s mass and radius)

  17. UNIVERSAL GRAVITATION • Orbits: gravity provides the centripetal force • stable orbit: Fc = Fg • orbit speed v = √Gme/r • orbit period T = 2pr/v • geosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

  18. UNIVERSAL GRAVITATION • Orbits • always falling but never reaching the ground • "Weightlessness"is NOT gravity-less • no gravity = no orbit • weightless isno normal force

  19. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

  20. ROTATIONAL MOTION • Rotational Motion: rotation around aninternal axis • angle, q: how much an object has rotated, unit: radian (rad) • 2p rad = 360º = 1 revolution (rev) • angular velocity, w = Dq/t: rate of rotation, unit: rad/s • frequency:revolutions per second, unit: Hertz, Hz • 1 Hz = 1 rev/s = 2p rad/s

  21. ROTATIONAL MOTION • angular acceleration, a= Dw/t: rate ofchange in rotation, unit: rad/s2 • Rotational Motion & Circular Motion • for any point on a spinning object: • v = rw • ac = rw2

  22. ROTATIONAL MOTION • torque, t: rotating effect of a force, unit: Nm • t = Fdsinq • d: "torque arm" or "lever arm“ • q: angle between F and d • torque direction: clockwise (c) or counterclockwise (cc)

  23. ROTATIONAL MOTION • Torque is zero when q = 0º or 180º • Torque is maximum when q =90º

  24. ROTATIONAL MOTION • Newton's Laws for Rotary Motion • A spinning object keeps spinning with constant angular velocity unless a net torque acts on it • A net torque causes an angular acceleration • For every action torque, there is an equal and opposite reaction torque

  25. d1 d2 F1 F2 ROTATIONAL MOTION • Rotational Equilibrium: object is balanced, or moves with constant angular velocity, due to no net torque • Stc = Stcc F2d2 = F1d1

  26. PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

  27. UNIT 3 REVIEW v = 2pr/T ac = v2/r Fc = mv2/r Fg = Gm1m2/r2 G = 6.67×10-11 Nm2/kg2 g = Gmp/r2 v = √Gmp/r me = 5.97×1024 kg re = 6.38×106 m w = Dq/t a= Dw/t v = rw ac = rw2 t = FdsinqStc = Stcc

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