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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 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 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 Astronaut’s Trainer for G-Force Electric Toothbrush/Hygienist’s 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 Doorknobs Tiller (garden or farm) Globe Dancer’s pirouette 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

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**Things that Turn Kids in Ring Around the Rosie Kids in Duck-Duck-Goose**

Skipit Jump-Rope Slinky ? Lasso Juicer Knobs (on binoculars)

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**Things That Turn Combine Auger 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

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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

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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**

Definition: Linear Velocity is distance/time: Ex 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, 2π rad/hour

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**Linear & Angular Velocity**

Deriving a formula which relates the two velocities: 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:**

Arc Length: Linear Velocity: Area of a Sector: Angular Velocity:

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**Variables: s, r, θ, A, v, t, ω Arc Length: s = r θ Area: A = ½ θ r2**

Def: Linear Velocity: v = s / t Def: Angular Velocity: ω = θ / t Relationship 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.

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