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The radian is the SI derived unit of an angle where

θ = d / r                              (1)

where

d = circular distance measured along the arc (m, in)

r = radius in circle (m, in)

Since the length of a circle is 2 π r, and the radius of the circle is r - the radians in a complete circle can be calculated to

θ = 2 π r / r

2 π

=~ 6.283185

One radian can be expressed in degrees as

1 rad = 360o / (2 π) = ~ 57.29578o                            (2a)

One radian can be expressed in revolutions as

1 rev = 1 / (2 π) = ~ 0.16                                 (2a)

One degree can be expressed in radians as

1o = 2 π / 360o = ~ 0.01745 radian                              (2c)

Note! - radians are used by default in angular expressions in most computer languages.

The radian is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.

degrees0o15o30o45o60o75o90o180o270o360o
radians 0 π/12 π/6 π/4 π/3 5π/12 π/2 π 3π/2
0 0.26 0.52 0.79 1.05 1.31 1.57 3.14 4.71 6.28

Degrees

### Angular Velocity

Converting angular velocity (ω) to other units

• ω = 1 rad/s = 9.55 r/min (rpm) = 0.159 r/s (rps)                                        (3)

RPM

Revolutions
(rpm)
Angular Velocity
0 0.0 0
10 1.0 60
20 2.1 120
30 3.1 180
40 4.2 240
50 5.2 300
60 6.3 360
70 7.3 420
80 8.4 480
90 9.4 540
100 10.5 600

### Example - Angular velocity 100 rad/s

An angular velocity of 100 rad/s can as indicated in the chart above be estimated to aprox. 950 rpm and 5700 deg/s.

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