ROTATIONAL MOTION Uniform Circular Motion

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ROTATIONAL MOTIONUniform Circular Motion
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Uniform Circular Motion

• Riding on a Ferris wheel or carousel ? Once a
  constant rate of rotation is reached (meaning the
  rider moves in a circle at a constant speed) ?
  UNIFORM CIRCULAR MOTION
• Recall Distinction
• Speed
• Magnitude or how fast an object moves
• Velocity
• Includes both magnitude AND direction
• Acceleration
• Change in velocity
• Preview Kinetic Books- 9.1

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Uniform Circular Motion

• Uniform Circular Motion
• Motion in a circle with constant speed
• Uniform refers to a constant speed
• Velocity is changing though!
• Length of the velocity vector does not change
  (speed stays constant), but the vectors
  direction constantly changes
• Since acceleration Change in velocity, the
  object accelerates as it moves around the track
• Instantaneous velocity is always tangent to the
  circle of motion

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Uniform Circular Motion

• Period
• Amount of time to complete one revolution
• Period for uniform circular motion
• T 2pr/v
• (2pr Distance around circle circumference)
• T period (s)
• r radius (m)
• v speed (m/s)
• p 3.14

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Uniform Circular Motion

• Tangential speed (vt)
• An objects speed along an imaginary line drawn
  tangent to the objects circular path
• Depends on the distance from the object to the
  center of the circular path
• Consider a pair of horses side-by-side on a
  carousel
• Each completes one full circle in the same time
  period but the outside horse covers more distance
  and therefore has a greater tangential speed

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Centripetal Acceleration

• Centripetal acceleration
• Acceleration due to change in direction in
  circular motion
• In uniform circular motion, acceleration
  CONSTANT
• Points toward the center of the circle ?
  perpendicular to the velocity vector
• Train goes around a track at a constant speed
• Trains velocity is changing because it is
  changing direction
• Change in velocity Acceleration

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Centripetal Acceleration

• Centripetal Acceleration
• Points toward the center of the circle
• ac vt2 /r
• ac Centripetal acceleration (m/s2)
• vt Tangential speed (m/s)
• r radius of circular path (m)

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Problem

• A car moves at a constant speed around a circular
  track. If the car is 48.2 m from the tracks
  center and has a centripetal acceleration of 8.05
  m/s2, what is the cars tangential speed?
• ac vt2 / r ? vt vacr ? vt v(8.05
  m/s2)(48.2m)
• vt 19.7 m/s

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Centripetal Force

• Forces Centripetal Acceleration
• Yo-yo swings in a circle ? it accelerates,
  because its velocity is constantly changing
  direction
• In order to have centripetal acceleration there
  must be a force present on the Yo-yo
• Force that causes centripetal acceleration points
  in the same direction as the centripetal
  acceleration ? Toward the center of the circle

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Centripetal Force

• Any force can be centripetal
• Yo-yo moves in a circle by the tension force in
  the string
• Gravitational force keeps satellites in circular
  orbits
• When forces act in this fashion, both tension and
  gravity ? Centripetal forces

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Newtons 2nd Law

• Newtons 2nd Law
• F ma
• When objects move in a circle ? Centripetal
  acceleration
• ac vt2 /r Now, plug this into F ma
• CENTRIPETAL FORCE (Fc)
• Fc m (vt2/r)
• Fc Newton
• m mass (kg)
• vt tangential speed (m/s)
• r radius of the circular path (m)
• Force points toward the center of the circle

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Problem

• A pilot is flying a small plane at 56.6 m/s in a
  circular path with a radius of 188.5 m. The
  centripetal force needed to maintain the planes
  circular motion is 1.89 x 104 N. What is the
  planes mass?
• Fc mvt2 / r
• m Fc r / vt2 (1.89 x 104 N)(188.5 m)/(56.6
  m/s)2
• m 1110 kg

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Centripetal Force

• Centripetal Force
• Acts at right angles to an objects circular
  motion
• Necessary for circular motion