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The radian is the SI derived unit of angle and can be expressed as
α = d / r (1)
where
α = radian
d = circular distance measured along the arc to the radius r
r = radius in circle
There are 2 π (pi) radians (about 6.283185) in a complete circle.
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.
| degrees | 0o | 15o | 30o | 45o | 60o | 75o | 90o | 180o | 270o | 360o |
| radians | 0 | π/12 | π/6 | π/4 | π/3 | 5π/12 | π/2 | π | 3π/2 | 2π |
| 0 | 0.26 | 0.52 | 0.79 | 1.05 | 1.31 | 1.57 | 3.14 | 4.71 | 6.28 |
Converting angular velocity to other units
| RPM | Angular Velocity | |
| (rad/s) | (deg/s) | |
| 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 |
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