# auto generate barcode vb net Linear and Angular Velocity in .NET framework Printer QR in .NET framework Linear and Angular Velocity

1.7 Linear and Angular Velocity
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Consider an object traveling at a constant velocity along a circular arc of radius r. Let s be the length of the arc traveled in time t. Let 2 be the angle (in radian measure) corresponding to arc length s. Linear velocity measures how fast the object travels. The linear velocity, v, of an object is computed by arc length s n t. time Angular velocity measures how fast the angle changes. The angular velocity, (the lower-case Greek central angle in radians u letter omega) of the object, is computed by v time t. The relationship between the linear velocity v and the angular velocity for an object with radius r is v where (NOTE: rv
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is measured in radians per unit of time and v is distance per unit of time. v and use the same unit of time and r and v use the same linear unit.)
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CHAPTER 1 Angles and Applications
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EXAMPLE 1.7 A bicycle with 20-in wheels is traveling down a road at 15 mi/h. Find the angular velocity of the wheel in revolutions per minute.
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Because the radius is 10 in and the angular velocity is to be in revolutions per minute (r/min), change the linear velocity 15 mi/h to units of in/min. v v To change 15 15 mi # 5280 ft # 12 in # 1 h mi h 1 h 1 mi 1 ft 60 min 15,840 rad rad v 1584 r 10 min min 15,840 in min
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to r/min, we multiply by 1/2 revolution per radian (r/rad). v 1584 rad min 1584 rad # 1 r 1 min 2p rad 792 r p min or 252 r/min
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EXAMPLE 1.8 A wheel that is drawn by a belt is making 1 revolution per second (r/s). If the wheel is 18 cm in diameter, what is the linear velocity of the belt in cm/s
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r 1s v
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1 # 2p rad 1 1 r rv 9(2p)
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2p rad/s 18p cm/s or 57 cm/s (See Probs. 1.11 to 1.15.)
SOLVED PROBLEMS
Use the directions for rounding stated on page 2. 1.1 Express each of the following angles in radian measure:
(a) 30 , (b) 135 , (c) 25 30 , (d) 42 24 35 , (e) 165.7 , (f) 3.85 , (g) 205 , (h) 18 30 , (i) 0.21 (a) 30 (b) 135 (c) 25 30 (d) 42 24 35 (e) 165.7 (f) (g) (h) (i) 3.85 205 18 30 0.21 30( /180) rad 135( /180) rad 25.5 42.41 /6 rad or 0.5236 rad 3 /4 rad or 2.3562 rad 0.4451 rad 0.7402 rad