1.4-1.5 Angle Measure in Degrees and Radians and Angular

1.4-1.5 Angle Measure in Degrees and Radians and Angular -...

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Unformatted text preview: Angle Measure in Degrees and Radians & Angular and Linear Velocity Sections 1.4 and 1.5 A central angle of a circle is an angle whose vertex is the center of the circle. 1 An arc of 1 degree is of a second. 360 A degree is subdivided into minutes. 1° = 60 ' A minute is subdivided into seconds. 1 = 60" ' Angle measures can be given in radians. When a central angle of a circle intercepts an arc that has the same length as the radius of the circle, the measure of this angle is defined to be one radian. r r r To change from degrees to radians, multiply by π ° 180 To change from radians to degrees, multiply by 180° π arc length angle = radius s θ= r arc length = radius • angle s = r •θ The angular displacement of a point is the angle through which the ray rotates. The angular velocity of a point on a revolving ray is the angular displacement per unit of time. θ ω= t The linear velocity V of a point on a revolving ray is the linear distance traveled b the point per unit of time. s V= t r •θ θ V= = •r t t V =ω•r Joke Time Joke Time What undergarment does Little Mermaid wear? An Alge­bra What does an acorn say when he grows up? Ge­om­etry ...
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