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Section 6-2
Linear and Angular Velocity
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Angular displacement – As any circular object rotates counterclockwise about its center, an object at the edge moves through an angle relative to its starting position known as the angle of rotation.
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• Determine the angular displacement in radians of 4.5 revolutions. Round to the nearest tenth.
• Note – Each revolution equals 2π radians.• For 4.5 revolutions, the number of radians is
= 28.3 radians
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• Determine the angular displacement in radians of 8.7 revolutions. Round to the nearest tenth.
• 8.7 x 2π=54.7 radians
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Angular velocity – the change in the central angle with respect to time as an object moves
along a circular path.
If an object moves along a circle during a time of t units, then the angular velocity, w, is given by
Where θ is the angular displacement in radians.
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Determine the angular velocity if 7.3 revolutions are completed in 5 seconds. Round to the nearest tenth.
•First calculate the angular displacement•7.3 x 2π = 45.9
•w=45.9/5 = 9.2 radians per second
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• Determine the angular velocity if 5.8 revolutions are completed in 9 seconds. Round to the nearest tenth.
• 4.0 radians/s
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• Angular velocity is the change in the angle with respect to time.
• Linear velocity is the movement along the arc with respect to time.
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Linear Velocity
• Linear velocity – distance traveled per unit of time
• If an object moves along a circle of radius of r units, then its linear velocity v is given by
• Where θ is the angular displacement therefore v=rw
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Determine the linear velocity of a point rotating at an angular velocity of 17π radians per second at a distance of 5 centimeters from the center of the rotating object. Round to the nearest tenth.
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Determine the linear velocity of a point rotating at an angular velocity of 31π radians per second at a distance of 15 centimeters from the center of the rotating object. Round to the nearest tenth.
1460.8 cm/s
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Pg 355