Convert Radians per second squared to Milliradians per second squared
Convert Radians per second squared (rad/s²) to Milliradians per second squared (mrad/s²) instantly and accurately.
Conversion Formula
mrad/s² = rad/s² × 1000
About Radians per second squared
The radian per second squared (rad/s²) is the SI coherent derived unit of angular acceleration. It appears in Newton's second law for rotation: τ = Iα, where torque τ is in N·m, moment of inertia I in kg·m², and angular acceleration α in rad/s². All engineering simulation tools (MATLAB, Simulink, ROS, FEM solvers) use rad/s² natively. A typical electric motor under full load accelerates at 10-100 rad/s². 1 rad/s² ≈ 57.296 °/s² ≈ 9.549 rpm/s.
About Milliradians per second squared
The milliradian per second squared (mrad/s²) equals 10⁻³ rad/s², the natural unit for robotic joint angular acceleration. Industrial robot arms (KUKA KR 1000, ABB IRB 8700) run joint acceleration profiles of 50-500 mrad/s²; CNC machine spindle synchronisation algorithms generate 1-100 mrad/s². Optical phased-array beam-steering systems also operate in this range. 1 mrad/s² = 10⁻³ rad/s² ≈ 0.0573 °/s² ≈ 9.549 × 10⁻³ rpm/s.
Quick Reference Table
| Radians per second squared (rad/s²) | Milliradians per second squared (mrad/s²) |
|---|---|
| 1 rad/s² | 1000 mrad/s² |
| 2 rad/s² | 2000 mrad/s² |
| 5 rad/s² | 5000 mrad/s² |
| 10 rad/s² | 10000 mrad/s² |
| 25 rad/s² | 25000 mrad/s² |
| 50 rad/s² | 50000 mrad/s² |
| 100 rad/s² | 100000 mrad/s² |