Linear & Angular Velocity Things that turn have both a

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Linear Angular Velocity

• Things that turn have both a
  linear velocity and an angular velocity.

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Things that Turn - Examples
tire on a car or bike
buckets on a waterwheel
teeth on a gear
can on a kitchen cabinet lazy susan
propeller on an airplane
horse on a Merry-Go-Round
fins on a fan or a windmill
earth on its axis
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Linear Angular Velocity - Examples
film on a projector or tape on a videotape
turntable in a microwave oven
blade on a lawnmower
Earth around the sun
seat on a Ferris wheel
rope around a pulley
a record on an old record player
drum/barrel in a clothes dryer
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Things that Turn - Examples

• lock on your locker
• hands on a clock
• roller brush on a vacuum cleaner
• tops gyroscopes dradle motor crankshaft
• blades in a blender rolly-polly bug
• roller skate wheels
• Carnival rides tilt-a-whirl, scrambler, etc.
• weather vane washing machine agitator

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Things That Turn

• propeller on a beanie
• mobile above a babys bed
• bit in a drill revolving door
• boomerang guinea pig wheel
• weather vane hula-hoop
• spinner in a table game Frisbee
• crank handle on a door handle
• knobs on a radio or television set

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Things That Turn

• Crank on an Ice Cream Freezer
• Blades in a garbage disposal
• Gears on a can opener
• CD in a CD player
• Weed eater
• Yo-Yo
• Screw on Cap on a pop-bottle

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Things That Turn

• Ball in a computer mouse
• Steering Wheel
• Basketball, baseball,football, etc
• Hammer Throw
• Sling (David Goliath)
• Electric Mixer
• Wheel of Fortune
• Price is Right Wheel

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Things that have Linear Angular Velocity

• Dog chasing his/her tail
• Astronauts Trainer for G-Force
• Electric Toothbrush/Hygienists Polisher
• Pottery Wheel
• Spinning Rims on a Car
• Food Processor
• Pizza Cutter
• Spin-the-Bottle

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Things That Turn

• Hurricanes, Tornados, Typhoons, etc.
• Water in a Whirlpool Spa or Jets in a Hot Tub
• Doorknobs
• Tiller (garden or farm)
• Globe
• Dancers pirouette turn or skaters turn
• Seat on a chair or barstool
• Paper towel roller

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Things that have linear angular velocity

• Pinwheel
• Pencil sharpener
• Lint roller
• Faucet handle
• Old time telephone dial
• Spit for a Hog Roast
• Hips of Hawaiian dancers
• Water in a flushing toilet
• Spiles on a Chain Saw

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Things that Turn

• Kids in Ring Around the Rosie
• Kids in Duck-Duck-Goose
• Skipit
• Jump-Rope
• Rowers arms rowing a boat
• Lasso
• Juicer
• Knobs (on binoculars)
• Pistol chamber

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Things That Turn

• Combine Auger/Rotor
• Kids around a Maypole
• Maps or Projector Screen around a roller
• Electrons around a Nucleus
• Conveyor Belt Sack Holder at Grocery
• Scotch tape in a dispenser
• Tetherball
• Rolling Pin
• Fingers on an IPod

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Things That Turn

• Electric Razor Blades
• Bullet from a Gun
• Concessions Hot Dog/Pretzel Turner
• Agitator in a Popcorn Kettle
• Roller for Highway Construction
• Flywheel
• Reel from a Rod-n-Reel Fishing Pole
• PTO on a tractor

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Things That Turn

• Anonometer
• Doppler Radar detector
• Siren/Light on a police car
• Conveyor belt
• Compass
• Hoosier Lottery wheel
• Loop on a Roller Coaster
• Shadow on a Sundial
• Crocodiles prey before eating

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• Arrow from a Bow
• Whirligigs
• Cooling Fan from a Computer/X-Box
• Trackball on a Mouse/Blackberry
• Cheerleader Fulldown (full twist cradle)
• English on a Pool Ball
• Fat Kid rolling down a Hill
• Snucker (spinning sucker candy)

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Things that Turn

• Air Currents from a moving Truck
• Fireworks (Jumping Jacks)
• Transparency Roller - Overhead Projector
• Winch
• Roullette Wheel
• Disco Ball
• Dizzy Bat
• Ball Socket Joint on the Human Body

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Things that Turn

• Spool of Thread
• Belt on an Engine
• Screwdriver
• Take-up Block/ Head Block
• Linda Blairs head in the Exorcist
• Rifle Barrel
• Track Runner
• Key Lock Mechanism
• Owl/Duck Head

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Things that Turn

• Satellites
• Helicopter Rotor Blades
• Diver (swimmer diving off board)
• Tumbleweed
• Car Wash Sprayer
• Stirring Coffee
• Chinese Plates
• Centrifuge ( Thanks, Hilary Burkhardt )
• New Years Eve Party Noisemaker

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Linear Angular Velocity
Definition
Linear Velocity is distance/time
Ex. 55 mph, 6 ft/sec, 27 cm/min, 4.5 m/sec
Definition
Angular Velocity is turn/time
The most common unit is RPM.
Ex. 6 rev/min, 360/day, 2p rad/hour
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Things that Turn

• Lathe
• Break-Dancer
• Cement Mixer
• Lights in a Lighthouse

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Linear Angular Velocity
Deriving a formula which relates the two
velocities
Recall Arc Length Formula?
Recognize Definition of Angular Velocity
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Linear Angular Velocity

• Find the angular velocity in R.P.M. of a
  microwave turntable if it turns through an angle
  of 36 each second.

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Linear Angular Velocity

• The cable lifting a garage door turns around a
  pulley at a rate of 20 cm per second. How long
  will it take to lift the door 2.2 meters?

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Linear Angular Velocity

• Find Joes linear velocity (in feet per min) on
  a Ferris Wheel turning 4 R.P.M. with a radius of
  30 feet.

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5 Formulas to KNOW/MEMORIZE
Arc Length
Linear Velocity
Area of a Sector
Angular Velocity
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Variables s, r, ?, A, v, t, ?

• Arc Length s r ?
• Area A ½ ? r2
• Def Linear Velocity v s / t
• Def Angular Velocity ? ? / t
• Relationship of v ? v r ?
• ? must be in RADIANS/time!
• Use RADIANS