CIRCULAR MOTION

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CIRCULAR MOTION
CIRCULAR MOTION

• The motion of
• things that rotate

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Whats this section about ?

• WHAT WOULD BE AN ANSWER TO THE FOLLOWING
• On a merry-go-round, which moves faster, the
  horse on the outside or the ostrich on the inside
  of the ride ?
• At 6-Flags Over Mid-America, why dont the people
  on the highland fling fall off when the platform
  is raised?
• When you swing something over your head at the
  end of a string and the string breaks, does the
  object continue in the same direction or does it
  fly directly outward?
• Why are the astronauts in the ISS (international
  space station) floating weightlessly about when
  future space missions will be in craft to
  rotating to create near normal gravity?

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ROTATION and REVOLUTION

• Any object (or person) that is turning does so
  about an imaginary straight line called an axis.
• For example, a carnival ride, a skater or a
  planet.
• If the axis is located with the body of (internal
  to) the object, the motion is called rotation or
  spin.
• If the object is turning around an external axis,
  the motion is called a revolution.

AXIS
rotation
CRASH !
revolution
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ROTATION and REVOLUTION

• Or, to put it another way,

The disc ROTATES about its internal
axis
Woah!
ROTATION
REVOLUTION
While the bug REVOLVES about an external axis
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ROTATION and REVOLUTION

• The planets follow this same rule
• They REVOLVE around the sun, while
  . ROTATING on their axes.

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A Trivial Science Note

• It takes 365 ¼ days for the earth to revolve once
  about the sun. This is why there is a leap year
  every 4 years, to catch up with the extra quarter
  day not used each year.
• It takes 24 hours for a point on the surface of
  the Earth to rotate back around directly under
  the sun again.
• But it takes only 23 hours and 56 minutes for a
  point on the surface of the Earth to rotate back
  under the stars again. This is because that as
  the Earth rotates, it revolves about a degree
  around the sun in its orbit.

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ROTATIONAL MOTION

• Lets start with a few definitions
• Linear Speed The distance moved per unit of
  time. The linear speed at a point on the outer
  edge of a rotating object is greater than the
  linear speed at any point nearer the axis because
  the point nearer the edge moves a greater
  distance in each revolution.
• Tangential Speed Refers to the speed of
  something moving along a circular path where the
  direction of motion is always tangent to the
  circle.
• Rotational Speed (angular speed) The number of
  rotations per unit of time (ex rpm, or r/sec.)
  also refers to the rate of rotation.

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ROTATIONAL MOTION
Three times as fast
Twice as fast
3
fast

• For Example
• The crankshaft in a car turns at around 3000
  rotations per minute (rpm) for optimal power.
• Any points on or in (all parts of) the crankshaft
  are turning at the same rotational speed.
• This works for any system where all parts have
  the same rotational speed (like a rotating disk
  or rod).
• The tangential speed (tangential velocity v),
  rotational speed (angular velocity ?), and
  radial distance from the axis of
  rotation (radius r ) are related in
  the equation v r . ?

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To Demonstrate that Tangential Speed Depends on
the Radius of a Rotating Object

• Consider what happens when a cylinder like a can
  and a conical (tapered) cylinder like a Styrofoam
  cup are rolled along a surface.
• The wide end of the cup has a greater radius,
  thus a greater linear speed and covers more
  distance as it rotates than the narrow end.
• The difference in the way these two objects roll
  shows that linear speed does depend on radius.

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QUESTIONS

• 1. Which part of the Earths surface has the
  greatest rotational . speed about the Earths
  axis?
• Which part has the greatest linear speed
  relative to the . Earths axis ?
• ANSWER
• All places on the surface of the Earth have
  the same . rotational speed.
• Because they are farther from the axis,
  regions along . the equator have the
  greatest linear (tangential) speed.

Were going faster !
Maybe, but were all going the same rotational
speed !
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QUESTIONS (Continued)

• 2. On a merry-go-round, animals at the edge are
  located 3 . times farther from the axis
  of rotation than the animals near . the
  center. If the animal near the center has a
  rotational . speed of 4 RPM and a
  tangential speed of 2 m/sec., what is . the
  rotational speed and the tangential speed of an
  animal . near the edge.
• All of the animals are rotating at 4 RPM,
  but the . tangential speed of
  the animals at the edge is 3 x 2 . 6
  m/sec since they are 3 times the distance from
  the . axis or center of the
  merry-go-round.
• 3. Train tracks are made up of a pair of rails.
  For straight-line . motion, the rails are
  the same length. But which rail is .
  longer for a curve, the outside rail or the
  inside rail?
• The outside rail is longer, it has the
  greater radius.

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Railroads Rolling on Tapered Wheels
The wheels of a train are tapered. When the train
makes a turn the smaller diameter part of the
taper rides on the inside track while the larger
part of the taper rides on the outer track. With
both wheels rotating at the same speed, the outer
wheel has a greater linear speed and so moves
around the curve.

• The wheels of a train are tapered.
• When the train makes a turn the smaller diameter
  part of the taper rides on the inside track while
  the larger part of the taper rides on the outer
  track.
• With both wheels rotating at the same speed, the
  outer wheel has a greater linear speed and so
  moves around the curve.

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Rolling on Tapered Wheels

• Like railroad wheels, a pair of styrofoam cups
  taped together rolls very well along a set of
  tracks, (but not on the surface of a table).
• The cups in this
  configuration are
  
  self-correcting.
• When the wider part
  of one cup
  rides the track,
  it moves faster than the
  narrow
  part of the other cup on the other
  track to steer the cups
  back toward
  the middle of the tracks.
• Cups arranged in the opposite
  configuration cannot stay on the tracks at
  all.

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CENTRIPETAL FORCE

• To make any object continuously travel in a
  circle, a continuous pull must be
  maintained inward toward the center of the
  circle.
• This center seeking or center directed force or
  tension is called CENTRIPETAL FORCE.
• CENTRIPETAL FORCE is
  not new, but simply the
  name
  given to any force directed at
  a right angle to
  the path of a
  moving object that tends to
  produce circular motion.
  

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CENTRIPETAL FORCE

• Gravitational force directed toward the center of
  the Earth holds the Moon in an almost circular
  orbit even across empty space
• Electrical forces directed inward toward the
  nucleus keep electrons in orbitals about an atom.
  
• The sideways acting friction between the road and
  the tires of a car provide the centripetal force
  to keep the car on a curved path around a corner.
  
• If there is not enough friction, the car will go
  into a skid.
• Centrifuges use centripetal force to separate
  different sized particles.

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Centripetal and Centrifugal Forces