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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
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 Winter '11
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 Calculus

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