Convert Radians per second squared to Nanoradians per second squared
Convert Radians per second squared (rad/s²) to Nanoradians per second squared (nrad/s²) instantly and accurately.
Conversion Formula
nrad/s² = rad/s² × 1000000000
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 Nanoradians per second squared
The nanoradian per second squared (nrad/s²) equals 10⁻⁹ rad/s², measuring imperceptibly gradual changes in rotation rate. Precision spacecraft attitude-control systems operate in this range during ultra-slow slew manoeuvres; GRACE-FO drag-free cold-gas thrusters produced angular accelerations at the nrad/s² scale. Ring laser gyroscopes monitoring Earth's polar motion require resolving nrad/s² variations. 1 nrad/s² = 10⁻⁹ rad/s² ≈ 1.02 × 10⁻⁹ rpm/s.
Quick Reference Table
| Radians per second squared (rad/s²) | Nanoradians per second squared (nrad/s²) |
|---|---|
| 1 rad/s² | 1000000000 nrad/s² |
| 2 rad/s² | 2 × 109 nrad/s² |
| 5 rad/s² | 5 × 109 nrad/s² |
| 10 rad/s² | 1 × 1010 nrad/s² |
| 25 rad/s² | 2.5 × 1010 nrad/s² |
| 50 rad/s² | 5 × 1010 nrad/s² |
| 100 rad/s² | 1 × 1011 nrad/s² |