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6.1.4 – Angular Speed, Linear Speed

6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r( θ ) Like a distance But, say we want to determine how fast an object is traveling on said arc . Angular Speed .

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6.1.4 – Angular Speed, Linear Speed

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  1. 6.1.4 – Angular Speed, Linear Speed

  2. Previously, we talked about the arc-length for a portion of any given circle; • AL = r(θ) • Like a distance • But, say we want to determine how fast an object is traveling on said arc

  3. Angular Speed • Angular Speed (frequency) = rate of travel along a circle’s circumference • Angle traveled over some time period • Angular Speed= ωAngle = θTime = t • ω =

  4. Example. A motorcycle wheel has a radius of 18 inches. The wheel travels at 150 rotations per minute. Find the angular speed of the wheel in inches per second. • 2π radians = 1 revolution

  5. Example. A gear has a radius of 3 inches and spins at 2500rpm. • A) Find the angular speed of the gear in rad/min. • B) Find the angular speed of the gear in rad/sec.

  6. Linear Speed • Typically, we will talk about the linear speed of a particular object • Linear Speed = the speed as if an object were traveling in only a linear direction • Linear Speed = v Radius = r • v = rω

  7. Example. An exercise bike is ridden such that it completes 85 revolutions per minute. A sensor is placed on the wheel such that the radius is 10 inches. • A) Find the angular speed in rad/minute • B) Find the linear speed in feet/minute

  8. Example. The earth takes about 23 hours and 56 minutes to complete on rotation on its’ axis. If the radius of earth is about 6370 KM, what is the linear speed in km/h of a person standing on the equator? • 56 minutes -> hour

  9. Assignment • Pg. 468 • 81-84, 94-96

  10. Arc Length = rϴ • Angular Speed (ω) = ϴ/t • Linear Speed = v = rω • Sector Area = • Pythagoren Theorem: a2 + b2 = c2

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