# Linear & Angular Velocity

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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 gearcan on a kitchen cabinet lazy susanpropeller on an airplanehorse on a Merry-Go-Roundfins on a fan or a windmillearth on its axis

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

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

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

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

Things That Turn

Ball in a computer mouseSteering WheelBasketball, baseball,football, etcHammer ThrowSling (David & Goliath)Electric MixerWheel of FortunePrice is Right Wheel

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

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

Things that have linear & angular velocity

PinwheelPencil sharpenerLint rollerFaucet handleOld time telephone dialSpit for a Hog RoastHips of Hawaiian dancersWater in a flushing toilet

Things that Turn

Kids in Ring Around the RosieKids in Duck-Duck-GooseSkipitJump-RopeSlinky ?LassoJuicerKnobs (on binoculars)

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

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

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.”

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

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:

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.

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?

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.

5 Formulas to KNOW/MEMORIZE:

s r

21

2A r

sv

tLinear Velocity:

Angular Velocity: t

v r

Arc Length:

Area of a Sector:

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

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.