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6.1 Angle Measures Angular and Linear Velocity and Arc Length

Chapter 6.1 – angular and linear velocity. 6.1 Angle Measures Angular and Linear Velocity and Arc Length. a few simple/silly word problems…. Yao Ming is about 8 feet tall. The local water tower has a height of about 5 “Yao Ming’s”. How many feet tall is the water tower?.

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6.1 Angle Measures Angular and Linear Velocity and Arc Length

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  1. Chapter 6.1 – angular and linear velocity 6.1 Angle MeasuresAngular and Linear Velocityand Arc Length

  2. a few simple/silly word problems… Yao Ming is about 8 feet tall. The local water tower has a height of about 5 “Yao Ming’s”. How many feet tall is the water tower?

  3. a few simple/silly word problems… My friend’s “soccer mom minivan” has a length of 14 feet (it’s HUGE). My friend’s house has a length of 10 “soccer mom minivans”. How long is my friend’s house? (yes this is silly but there’s a point to this)

  4. so this is where it gets real (and why we use radians) The earth has a radius of about 4000 miles. An airplane flies from North America to Europe, and covers an angular distance of 2.0 radians. (that’s a little less than 120 degrees) How many miles did the plane travel?(hint: 2.0 radians means 2.0 “radiuses”!)

  5. and one more… (this one requires some dimensional analysis) A wagon wheel rolls down a hill and, in the process, makes 10 full revolutions (each revolution is 2π radians). If the wheel has a radius of 30 inches, how many FEET did the wheel roll down the hill?

  6. Chapter 6.1 – angular and linear velocity Length of a Circular Arc Θ has to be in radians!! • Find the length of an arc of a circle with radius 10 m that subtends a central angle of 30o. • A central angle θ in a circle of radius 4 m is subtended by an arc of length 6m. Find the measure of θ in radians.

  7. Chapter 6.1 – angular and linear velocity Area of a Circular Sector • Find the area of a sector of a circle with central angle 60o if the radius of the circle is 3 m. Θ has to be in radians!!

  8. Chapter 6.1 – angular and linear velocity Circular Motion • Angular Speed (ω): Always a circular measurement over time. • degrees per second • Radians per minute • Revolutions per minute (RPM) • Rotations per hour

  9. Chapter 6.1 – angular and linear velocity Circular Motion • Linear Speed (v): Always a linear measurement over time. • mph (miles per hour) • Feet per second • Inches per minute • Kilometers per hour • r=radius ω=angular velocity

  10. Chapter 6.1 – angular and linear velocity Jon and Kate are riding on a Ferris wheel. Jon doesn’t want to ride with Kate, and gets off of the ride. He observes that it takes 50 seconds to make a complete revolution (that is, to travel one complete circle). Their seat is 30 feet from the axle of the wheel. • What is their angular velocity in revolutions per minute? • in degrees per minute? • in radians per minute?

  11. Chapter 6.1 – angular and linear velocity Kate gets mad at Jon, and puts a rock in her sling and starts whirling it around. She realizes that in order for the rock to hit Jon, it must leave her sling at a speed of 100 feet per second. (is this a measure of linear velocity or angular velocity?) Her sling is swung in a circular path of radius of 5 feet. What must the angular velocity be in order for Kate’s rock to reach Jon? Note: the McNeil math department strong discourages the use of slingshots and stones in the settling of domestic disputes.

  12. Chapter 6.1 – angular and linear velocity Jon gets in his car to get the heck away from Kate. The rear wheels on his 350z sports car spin at a rate of 5000 revolutions per minute. If a wheel has a radius of 9 inches, how fast is the wheel turning in miles per hour? (this one involves a lot of conversions. Hint: 1 mile = 5280 feet) Please buckle up and drive safely. Getting hit by a rock hurts… but so does getting into a car accident.

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