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Warm up

Warm up. Change to radian measure in terms of π . Change to degrees. Evaluate Given the central angle of the length of its intercepted arc in a circle of radius 19cm. Round to the nearest tenth.

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Warm up

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  1. Warm up Change to radian measure in terms of π. Change to degrees. Evaluate Given the central angle of the length of its intercepted arc in a circle of radius 19cm. Round to the nearest tenth. Find the area of a sector if the central angle measures and the diameter of the circle is 19 meters. 56.7cm

  2. Section 6-2Linear and angular velocities • Essential Questions How is one revolution measured? What is the difference between angular and linear velocity? Vocabulary: Angular Displacement Angular Velocity Dimensional Analysis Linear Velocity

  3. Example 1 • Determine the angular displacement in radians of 4.5 revolutions. Remember each revolution equals Angular velocity is the ratio of change in the central angle to the time required for the change and is represented by a lower case Omega (ω).

  4. Example 2 • Determine the angular velocity if 7.3 revolutions are completed in 5 seconds. Round to the nearest tenth. Dimensional analysis is a way to avoid mistakes when computing with units of measure. Unit labels are treated as mathematical factors that can be divided out

  5. Example 3 • The Children’s Museum in Indianapolis, Indiana, houses an antique carousel. The carousel contains three concentric circles of animals. The inner circle of animals is approximately 11 feet from the center, and the outer circle of animals is approximately 20 feet from the center. The carousel makes rotations per minute. Determine the angular and linear velocities of someone riding an animal in the inner circle and of someone riding an animal in the same row in the outer circle.

  6. Example 4 • Determine the linear velocity of a point rotating at an angular velocity of 17π radians per second at a distance of 5cm from the center of the rotating object.

  7. Example 5 • The tires on a race car have a diameter of 30 inches. If the tires are turning at a rate of 2000 revolutions per minute, determine the race car’s speed in miles per hour.

  8. Exit Ticket • 1. Compare and contrast linear and angular velocity. • 2. Use that knowledge to explain how two people on a rotating carousel can have the same angular velocity, but different linear velocities. • 3. Write one thing that you learned in class today. • 4. Write one thing that you still have questions about.

  9. Homework • P355 # 13-35 Odd, 37-39A, 41, 43-51A

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