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 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. Linear & Angular Velocity
Deriving a formula which
relates the two velocities:
Definition of Linear Velocity:
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.