Unit 1 - Objective 4 - Radian Measure Applications
Quick Review

Use the following formulas. Remember that the angle theta always needs to be in radians.

Arc length = (angle)(radius)
S = theta 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 = 2 pi radians = 360°
1 rpm = 1 revolution per minute = 2 pi 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 theta
          = (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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