Presentation on theme: "Linear & Angular Velocity"— Presentation transcript:
1 Linear & Angular Velocity Things that turn have both a linear velocity and an angular velocity.
2 Things that Turn - Examples tire on a car or bikebuckets on a waterwheelteeth 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
3 Linear & Angular Velocity - Examples film on a projector or tape on a videotapeturntable in a microwave ovenblade on a lawnmowerEarth around the sunseat on a Ferris wheelrope around a pulleya record on an old record playerdrum/barrel in a clothes dryer
4 Things that Turn - Examples lock on your lockerhands on a clockroller brush on a vacuum cleanertops & gyroscopes & dradle motor crankshaftblades in a blender rolly-polly bugroller skate wheelsCarnival rides: tilt-a-whirl, scrambler, etc.weather vane washing machine agitator
5 Things That Turn propeller on a beanie mobile above a baby’s bed bit in a drill revolving doorboomerang guinea pig wheelweather vane hula-hoopspinner in a table game Frisbeecrank handle on a door handleknobs on a radio or television set
6 Things That Turn Crank on an Ice Cream Freezer Blades in a garbage disposalGears on a can openerCD in a CD playerWeed eaterYo-YoScrew on Cap on a pop-bottle
7 Things That Turn Ball in a computer mouse Steering Wheel Basketball, baseball,football, etcHammer ThrowSling (David & Goliath)Electric MixerWheel of FortunePrice is Right Wheel
8 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
9 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
10 Things that have linear & angular velocity PinwheelPencil sharpenerLint rollerFaucet handleOld time telephone dialSpit for a Hog RoastHips of Hawaiian dancersWater in a flushing toilet
11 Things that Turn Kids in Ring Around the Rosie Kids in Duck-Duck-Goose SkipitJump-RopeSlinky ?LassoJuicerKnobs (on binoculars)
12 Things That Turn Combine Auger Kids around a Maypole Maps or Projector Screen around a rollerElectrons around a NucleusConveyor Belt & Sack Holder at GroceryScotch tape in a dispenserTetherballRolling Pin
13 Things That Turn Electric Razor Blades Bullet from a Gun Concessions: Hot Dog/Pretzel TurnerAgitator in a Popcorn KettleRoller for Highway ConstructionFlywheelReel from a Rod-n-Reel Fishing Pole
14 DefinitionAngular 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.”
15 Linear & Angular Velocity Definition:Linear Velocity is distance/time:Ex mph, 6 ft/sec, 27 cm/min, 4.5 m/secDefinition:Angular Velocity is turn/time:The most common unit is RPM.Ex. 6 rev/min, 360°/day, 2π rad/hour
16 Linear & Angular Velocity Deriving a formula whichrelates the two velocities:Definition of Linear Velocity:Recall Arc Length FormulaRecognize Definition of Angular Velocity:
17 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.
18 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?
19 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.
20 5 Formulas to KNOW/MEMORIZE: Arc Length:Linear Velocity:Area of a Sector:Angular Velocity:
21 Variables: s, r, θ, A, v, t, ω Arc Length: s = r θ Area: A = ½ θ r2 Def: Linear Velocity: v = s / tDef: Angular Velocity: ω = θ / tRelationship of v & ω: v = r ωω must be in RADIANS/time!Use RADIANS
22 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.