linear & angular velocity
DESCRIPTION
Linear & Angular Velocity. Things that turn have both a linear velocity and an angular velocity. 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. - PowerPoint PPT PresentationTRANSCRIPT
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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 gearcan on a kitchen cabinet lazy susanpropeller on an airplanehorse on a Merry-Go-Roundfins on a fan or a windmillearth 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 lawnmowerEarth around the sun
rope around a pulleyseat on a Ferris wheel
a record on an old record playerdrum/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 baby’s 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 FreezerBlades in a garbage disposalGears on a can openerCD in a CD playerWeed eaterYo-YoScrew on Cap on a pop-bottle
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Things That Turn
Ball in a computer mouseSteering WheelBasketball, baseball,football, etcHammer ThrowSling (David & Goliath)Electric MixerWheel of FortunePrice is Right Wheel
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Things that have Linear & Angular Velocity
Dog chasing his/her tailAstronaut’s Trainer for G-ForceElectric Toothbrush/Hygienist’s PolisherPottery WheelSpinning Rims on a CarFood ProcessorPizza CutterSpin-the-Bottle
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Things That Turn
Hurricanes, Tornados, Typhoons, etc.Water in a Whirlpool SpaDoorknobsTiller (garden or farm)GlobeDancer’s pirouette turnSeat on a chair or barstoolPaper towel roller
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Things that have linear & angular velocity
PinwheelPencil sharpenerLint rollerFaucet handleOld time telephone dialSpit for a Hog RoastHips of Hawaiian dancersWater in a flushing toilet
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Things that Turn
Kids in Ring Around the RosieKids in Duck-Duck-GooseSkipitJump-RopeSlinky ?LassoJuicerKnobs (on binoculars)
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Things That Turn
Combine AugerKids around a MaypoleMaps or Projector Screen around a rollerElectrons around a NucleusConveyor Belt & Sack Holder at GroceryScotch tape in a dispenserTetherballRolling Pin
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Things That Turn
Electric Razor BladesBullet from a GunConcessions: Hot Dog/Pretzel TurnerAgitator in a Popcorn KettleRoller for Highway ConstructionFlywheelReel from a Rod-n-Reel Fishing Pole
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Definition
Angular Displacement: The distance an object moves around a circle.
Angular velocity: The ratio of the change in a central angle to the time required for the change. “How fast the object moves around the edge of a circle.”
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Linear & Angular Velocity
t
sv Linear Velocity is distance/time:
Angular Velocity is turn/time:t
Definition:
Definition:
Ex. 55 mph, 6 ft/sec, 27 cm/min, 4.5 m/sec
The most common unit is RPM.
Ex. 6 rev/min, 360°/day, 2π rad/hour
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Linear & Angular Velocity
t
rv
Deriving a formula which relates the two velocities:
rv
t
sv Definition of Linear Velocity:
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 Ben’s 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:
s r
21
2A r
sv
tLinear Velocity:
Angular Velocity: t
v r
Arc Length:
Area of a Sector:
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Variables: s, r, θ, A, v, t, ω
Arc Length: s = r θArea: A = ½ θ r2
Def: Linear Velocity: v = s / t
Def: Angular Velocity: ω = θ / tRelationship of v & ω: v = r ω
ω must be in RADIANS/time! Use RADIANS
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Example:
Determine the linear velocity of a point rotating at an angular velocity of 17pi radians per second at a distance of 5cm from the center of the rotating object. Round to the nearest tenth.