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

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

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: