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## 6.1.4 – Angular Speed, Linear Speed

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**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**• Angular Speed (frequency) = rate of travel along a circle’s circumference • Angle traveled over some time period • Angular Speed= ωAngle = θTime = t • ω =**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**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.**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**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**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**Assignment**• Pg. 468 • 81-84, 94-96**Arc Length = rϴ**• Angular Speed (ω) = ϴ/t • Linear Speed = v = rω • Sector Area = • Pythagoren Theorem: a2 + b2 = c2