PHYSICS UNIT 3: CIRCULAR

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PHYSICS UNIT 3 CIRCULAR ROTATIONAL MOTION
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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)

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CIRCULAR MOTION

• all turning objects have centripetal (center-
  seeking) acceleration

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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

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CIRCULAR MOTION

• no centripetal force no turning (linear motion)

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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.
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CIRCULAR MOTION

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

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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
  centripetal force

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CIRCULAR MOTION

• centrifugal force only exists within the turning
  objects frame of reference - it is a fictitious
  force

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CIRCULAR MOTION

• Frames of Reference - things moving on a rotating
  object seem to be made to turn by the coriolis
  force

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PHYSICS

• UNIT 3 CIRCULAR ROTATIONAL MOTION

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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

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PHYSICS

• UNIT 3 CIRCULAR ROTATIONAL MOTION

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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

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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, 6.6710-11
  Nm2/kg2
• gravity is only significant for very large masses

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UNIVERSAL GRAVITATION

• acceleration due to gravity, g Gme/r2
• Also known as the gravitational field strength
• me earth's mass (5.971024 kg)
• r distance from earths center (6.38106 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 planets mass and radius)

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UNIVERSAL GRAVITATION

• Orbits gravity provides the centripetal force
• stable orbit Fc Fg
• orbit speed v vGme/r
• orbit period T 2pr/v
• geosynchronous orbit T 24.0 hrs, satellite
  stays over same position on earth

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UNIVERSAL GRAVITATION

• Orbits
• always falling but never reaching the ground
• "Weightlessness" is NOT gravity-less
• no gravity no orbit
• weightless is no normal force

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PHYSICS

• UNIT 3 CIRCULAR ROTATIONAL MOTION

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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

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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

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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)

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ROTATIONAL MOTION

• Torque is zero when q 0º or 180º
• Torque is maximum when q 90º

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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

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ROTATIONAL MOTION

• Rotational Equilibrium object is balanced, or
  moves with constant angular velocity, due to no
  net torque
• Stc Stcc

• F2d2 F1d1

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PHYSICS

• UNIT 3 CIRCULAR ROTATIONAL MOTION

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UNIT 3 REVIEW

• v 2pr/T ac v2/r Fc mv2/r
• Fg Gm1m2/r2 G 6.6710-11 Nm2/kg2
• g Gmp/r2 v vGmp/r
• me 5.971024 kg re 6.38106 m
• w Dq/t a Dw/t
• v rw ac rw2
• t Fdsinq Stc Stcc