Unit 1  Objective 4  Radian Measure Applications
Quick Review
Use the following formulas. Remember that the angle always needs to be in radians.
Arc length = (angle)(radius)
S = r 


Area of a sector of a circle



Linear velocity = (radius)(angular velocity)
V = rw
(ft/sec) = (ft)(radians/sec)
(cm/sec) = (cm)(radians/sec) 

Note:
1 revolution = radians = 360°
1 rpm = 1 revolution per minute = radians per minute = 360° per minute
Example 1
Find the arc length and area of a sector of a circle with radius 2.7 cm and central angle 1.3 radians.
Solution:
Arc length
Use S = r
= (2.7)(1.3) = 3.51 cm
Area
Example 2
A steel cylinder 8cm in diameter is to be machined in a lathe. If the desired linear velocity of the cylinder's surface is 80.5 cm/sec, at how many rpm should it rotate?
Solution:
We need 4 as the radius since 8 is the diameter.
Use V = rw
80.5 = 4w
80.5/4 = w
20.125 rad/sec = w
Now 1 rpm is radians per minute. We use the proportion:
If we cross multiply:
So:
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