Circular Motion

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Chapter 9

• Circular Motion

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Did You Know?

• Did You Know? The tilt of the Earth on its axis
  and the Earth's revolution cause the seasons NOT
  the Earth's proximity to the Sun.

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Rotations Revolutions
An axis is the straight line around which
rotation takes place.

• Revolution is a spin about an axis outside the
  body.
• a wheel rim
• a satellite orbiting the earth

• Rotation is a spin about an axis located within
  the body
• a wheel
• a satellite

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Rotation and Revolution

• The Ferris wheel turns about an axis.
• The Ferris wheel rotates, while the riders
  revolve about its axis.

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Rotations Revolutions

• Does a tossed football rotate or revolve?
• rotates (spins)
• Does a ball whirled overhead at the end of a
  string rotate or revolve?
• revolves about you

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Rotation and Revolution

• Earth undergoes both types of rotational motion.
• It revolves around the sun once every 365 ¼ days.
• It rotates around an axis passing through its
  geographical poles once every 24 hours.

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Rotational Speed Tangential Speed

• Merry-go-around
• Rotational speed is same anywhere on the ride
  (same revolutions/second)
• Linear speed is tangent to the curved path and
  different depending on where you ride.
• Linear speed is perpendicular to the radial
  direction is called tangential velocity.
• Conceptual Physics Demo - Rotational Speed -
  YouTube

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Speed

• Which part of the turntable moves fasterthe
  outer part where the ladybug sits or a part near
  the orange center?
• It depends on whether you are talking about
  linear speed or rotational speed.
• Linear (tangential) speed depends on rotational
  speed and the distance from the axis of rotation.
  

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Rotational Speed

• All parts of the turntable rotate at the same
  rotational speed.
• A point farther away from the center travels a
  longer path in the same time and therefore has a
  greater tangential speed.
• A ladybug sitting twice as far from the center
  moves twice as fast.

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Circular Motion.

• In symbol form,
• v r?
• where v is tangential speed and ? (pronounced oh
  MAY guh) is rotational speed.
• You move faster if the rate of rotation increases
  (bigger ?).
• You also move faster if you are farther from the
  axis (bigger r).

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Conservation of Angular Momentum

• DEMO Conservation of angular momentum - YouTube
• angular momentum rotational inertia
  rotational velocity
• L I w
• Newton's first law for rotating systems
• A body will maintain its state of angular
  momentum unless acted upon by an unbalanced
  external torque.

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• The linear speed is directly proportional to both
  rotational speed and radial distance.
• v w r
• What are two ways that you can increase your
  linear speed on a rotating platform?
• Answers
• Move away from the rotation axis.
• Have the platform spin faster.

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Tangential Speed

•  

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Rotational Speed Tangential Speed

• Two coins on turn table, one near center and
  other near edge.
• Outer coin has
• greater linear speed.
• Both have same
• rotational speed revolutions per second.
• Examples
• See design on hub cap but not on the tire.
• Crack-the-whip end person.

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Tangential Speed (Linear Velocity)

• Swinging Meterstick
• How fast at any given moment is the 100-cm mark
  moving compared to the 50-cm mark?
• The 100-cm mark is twice as far from the center
  of rotation than the 50-cm mark and has twice the
  linear speed.
• Why does a flyswatter have long handle?
• Long handle amplifies the speed of your hand.

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Tapered Wheels of Rail Road Cars

• Do Doing Physics pg. 125 126

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Rotational Speed
A tapered cup rolls in a curve because the wide
part of the cup rolls faster than the narrow part.
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10.2 Rotational Speed

• A pair of cups fastened together will stay on the
  tracks as they roll.
• The cups will remain on the track.
• They will center themselves whenever they roll
  off center.

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Rotational Speed
When the pair rolls to the left of center, the
wider part of the left cup rides on the left
track while the narrow part of the right cup
rides on the right track. This steers the pair
toward the center. If it overshoots toward the
right, the process repeats, this time toward the
left, as the wheels tend to center themselves.
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Rotational Speed
When a train rounds a curve, the wheels have
different linear speeds for the same rotational
speed.
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Rotational Speed
When a train rounds a curve, the wheels have
different linear speeds for the same rotational
speed.
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Centripetal Force
Centripetal means toward the center. The force
directed toward a fixed center that causes an
object to follow a circular path is called a
centripetal force. Example If you whirl a tin
can on the end of a string, you must keep pulling
on the stringexerting a centripetal force. The
string transmits the centripetal force, pulling
the can from a straight-line path into a circular
path
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Centripetal Force
The force exerted on a whirling can is toward the
center. No outward force acts on the can.
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Remember

•  

• v w r

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Centripetal Acceleration and Centripetal Force

• Centripetal Acceleration (ac)- acceleration
  directed toward the center of the circle
• change in velocity per unit of time
• rate at which velocity is changing
• velocity is changing because the object is
  constantly changing its direction as it follows a
  curved path
• centripetal acceleration (linear speed)2 ac
  v2 symbolac
• radius r unit m/
  s2
• if mass is being accelerated toward the center of
  a circle, it must be acted upon by an unbalance
  net force that gives it this acceleration
• Joe is sitting 2m from the center of a
  merry-go-round that has a frequency of 1. 25 Hz
  (Hertz is one revolution per second). What is
  Joes centripetal acceleration? What is the
  direction of the centripetal acceleration?

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Centripetal Force

•  

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Centripetal Force

• Whirling Can at End of a String
• The string pulls radially inward on the can. By
  Newtons Third Law, the can pulls outward on the
  string so there is an outward-acting force on
  the string. This outward force does not act on
  the can. ONLY inward force on the can.

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Spinning Washer

• The tub wall exerts Fc on the clothes forcing it
  into a circular path, but not the water. Water
  escapes bcs no Force acting on it.so water stays
  in straight line path perpendicular or tangent to
  the curve.

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Centrifugal ForceCenter-fleeing or Away from
Center

• An apparent outward force on a rotating or
  revolving body.
• It is fictitious in the sense that it is not part
  of an interaction but is due to the tendency of a
  moving body to move in a straight-line path due
  to inertia
• Is useful only in a rotating frame of reference
• The inward push feels like an outward pull to
  the object in a rotating system (as if a big mass
  were out there causing gravity)
• Not a real force there is no interaction (there
  is no mass out there pulling on it).
• There is no action reaction pair of forces

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Misconception

• BIG MISCONCEPTION centrifugal force pulls
  outward on an object in a circular path
• fig 9.7 then string breaks....
• misconception.....centrifugal force pulls can
  from its circular path
• reality....can goes off in a straight-line path
  tangent to circle because
• there is NO FORCE acting on can anymore
• fig 9.8 only the force from the string acts on
  the can to pull the can inward there is no
  outward
• force acting on the can

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Centrifugal Forces
The only force that is exerted on the whirling
can (neglecting gravity) is directed toward the
center of circular motion. This is a centripetal
force. No outward force acts on the can.
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The can provides the centripetal force necessary
to hold the ladybug in a circular path.
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Centrifugal Force

• A person in a spinning space habitat feels a
  force like that of gravity and does pushups just
  like on earth.
• Is the force centripetal or centrifugal?
• How is it different than gravity?
• Conceptual Physics Simulated Gravity - YouTube

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Centrifugal Forces
The can presses against the bugs feet and
provides the centripetal force that holds it in a
circular path. The ladybug in turn presses
against the floor of the can. Neglecting
gravity, the only force exerted on the ladybug is
the force of the can on its feet. From our
outside stationary frame of reference, we see
there is no centrifugal force exerted on the
ladybug.
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Rotational Inertia

• An object rotating about an axis tends to remain
  rotating unless interfered with by some external
  influence.
• This influence is called torque.
• Rotation adds stability to linear motion.
• Examples
• spinning football
• bicycle tires
• Frisbee

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• The greater the distance between the bulk of an
  object's mass and its axis of rotation, the
  greater the rotational inertia.
• Examples
• Tightrope walker
• Metronome

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Torque

• Torque is the product of the force and lever-arm
  distance, which tends to produce rotation.
• Torque force lever arm
• Examples
• wrenches
• see-saws

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Center of Mass

• The center of mass of an object is the average
  position of mass.
• Objects tend to rotate about their center of
  mass.
• Examples
• Meter stick
• Rotating Hammer

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Stability

• For stability center of gravity must be over area
  of support.
• Examples
• Tower of Pisa
• Touching toes with back to wall
• Meter stick over the edge
• Rolling Double-Cone

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Direction of Motion
Centrifugal Force
Centripetal Force
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Centripetal Force

• is applied by some object.
• Centripetal means "center seeking".

Centrifugal Force

• results from a natural tendency.
• Centrifugal means "center fleeing".

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• What is that force that throws you to the right
  if you turn to the left in your car?
• centrifugal force.
• What is that force that keeps you in your seat
  when you turn left in your car?
• centripetal force.

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Examples
Centripetal Force
Centrifugal Force

• water in bucket
• moon and earth
• car on circular path
• coin on a hanger
• jogging in a space station

• Bucket
• Earths gravity
• Road Friction
• Hanger
• Space Station Floor

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Example Question

• Two ladybugs are sitting on a phonograph record
  that rotates at 33 1/3 RPM.
• 1. Which ladybug has a great linear speed?
• A. The one closer to the center.
• B. The one on the outside edge.
• C. The both have the same linear speed

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Example Question

• Two ladybugs are sitting on a phonograph record
  that rotates at 33 1/3 RPM.
• 1. Which ladybug has a great linear speed?
• A. The one closer to the center.
• B. The one on the outside edge.
• C. The both have the same linear speed

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Example Question

• Two ladybugs are sitting on a phonograph record
  that rotates at 33 1/3 RPM.
• 2. Which ladybug has a great rotational speed?
• A. The one closer to the center.
• B. The one on the outside edge.
• C. The both have the same rotational speed

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Example Question

• You sit on a rotating platform halfway between
  the rotating axis and the outer edge.
• You have a rotational speed of 20 RPM and a
  tangential speed of 2 m/s.
• What will be the linear speed of your friend who
  sit at the outer edge?

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Example Question

• You sit on a rotating platform halfway between
  the rotating axis and the outer edge.
• You have a rotational speed of 20 RPM and a
  tangential speed of 2 m/s.
• What will be the linear speed of your friend who
  sit at the outer edge?
• A. 4m/s
• B. 2m/s
• C. 20 RPM
• D. 40 RPM
• E. None of these

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Example Question

• You sit on a rotating platform halfway between
  the rotating axis and the outer edge.
• You have a rotational speed of 20 RPM and a
  tangential speed of 2 m/s.
• What will be the rotational speed of your friend
  who sit at the outer edge?
• A. 4m/s
• B. 2m/s
• C. 20 RPM
• D. 40 RPM
• E. None of these

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End of Chapter