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Linear & Angular Velocity

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.

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Linear & Angular Velocity

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  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 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. Things that Turn • Kids in Ring Around the Rosie • Kids in Duck-Duck-Goose • Skipit • Jump-Rope • Slinky ? • Lasso • Juicer • Knobs (on binoculars)

  12. 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

  13. 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

  14. 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.”

  15. 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, 2π rad/hour

  16. Definition of Linear Velocity: Linear & Angular Velocity Deriving a formula which relates the two velocities: Recall Arc Length Formula Recognize 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 / t Def: Angular Velocity: ω = θ / t • Relationship of v & ω: v = r ω ω 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.

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