Circular Motion

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Circular Motion

• Spinning Things

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Students Give Examples of Spinning Things.
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Measuring Circles

• Rotations and Revolutions
• Degrees (0-360)
• Radians

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How?
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(No Transcript)
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How Fast? Angular Speed

• Recall speed
• Possible Units m/s, ft/s, km/hr, miles/hr

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Angular Speed

• (rad)/s
• Degrees/s
• Rpm, rev/s, rot/s

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Angular Velocity Sample Problems

• It takes a merry-go-round 4.56 seconds to make
  one complete turn. What is its angular velocity?
• What is the angular velocity of the earth about
  its axis?
• A ballet dancer can make 3.25 pirouettes in a
  second. What is her angular velocity?
• An old-fashioned LP album is called a 45. It
  makes 45 revolutions per minute. What is its
  angular velocity in (rad)/s?

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Relationship Between Linear Velocity and Angular
Velocity

• Where do you sit on the merry-go-round or the
  swings at Lost Kennywood? Chances are, if you are
  a daring person you probably sit on the outside.
  When you were really young and scared of the
  ride, you probably sat on the inside. Why?

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Linear v. Angular Velocity

• Linear velocity angular velocity x distance
  from the spin axis.
• In other words
• v r

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Angular and Linear Velocity

• It takes the Aero 360 at Kennywood .83 seconds
  to make one complete turn. What is its angular
  velocity?

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Angular Acceleration
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Angular Acceleration

• Recall linear acceleration
• Speed change, direction change or both
• What happens when you turn a ceiling fan on?
  (Explain in detail.)
• THATS Angular Acceleration !!!

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Angular Acceleration Problems

• A ceiling fan goes from rest to 2.38 (rad)/s in
  45 seconds. What was its angular acceleration?
• A ceiling fan goes from 2.38 (rad)/s to rest in a
  minute and 16 seconds. What was its angular
  acceleration?
• Is angular acceleration a vector or scalar
  quantity?
• A Blackhawk helicopter blade goes from rest to
  1500 rpms in 23 seconds. What is its angular
  acceleration?
• If the propeller is 7.35 m long, what is the
  linear velocity of the tip of the propeller?