Convert between rad/s², deg/s², rev/s² and rev/min².
Angular acceleration describes how quickly an object's rotational speed changes. The SI unit is radian per second squared (rad/s²). It is widely used in robotics, automotive engineering, and physics.
| Unit | In rad/s² |
|---|---|
| 1 deg/s² | 0.017453 rad/s² |
| 1 rev/s² | 6.28318 rad/s² |
| 1 rev/min² | 0.001745 rad/s² |
Acceleration Converter • Angular Velocity Converter • Speed Converter
Angular acceleration measures how quickly a rotating object changes its rotational speed. Units are radians per second squared (rad/s²) or degrees per second squared (°/s²). When you start a ceiling fan, the blades go from 0 RPM to full speed — that change in rotational velocity over time is angular acceleration. In engineering, it matters for electric motors, flywheels, robotic joints, and gyroscopes.
The relationship between angular acceleration (α) and linear acceleration (a) at radius r is: a = α × r. A point on the rim of a large wheel experiences greater linear acceleration than one near the centre, even with the same angular acceleration.
| Unit | rad/s² | Use case |
|---|---|---|
| 1 rad/s² | 1.000 | SI standard |
| 1 °/s² | 0.01745 | Robotics |
| 1 rev/s² | 6.2832 | Motor specs |
| 1 rev/min² | 0.001745 | Industrial machinery |
Angular acceleration is critical in motor design — a motor that needs to spin up quickly must deliver high angular acceleration. Electric motors typically reach full speed in milliseconds; large industrial motors may take seconds. In robotics, joint angular acceleration determines how fast a robot arm can move between positions. In vehicle dynamics, wheel spin-up during a drag race is controlled by traction control systems limiting angular acceleration to prevent wheel slip. Gyroscopes in smartphones and aircraft instruments measure angular acceleration to determine orientation changes.
Angular acceleration measures how quickly an object's rotational speed changes, expressed as angle per time squared. The SI unit is radians per second squared (rad/s²). Other units include degrees per second squared (°/s²), revolutions per minute per second (rpm/s), and revolutions per second squared (rev/s²). The conversion: 1 rev/s² = 2π rad/s² ≈ 6.2832 rad/s²; 1 °/s² = π/180 rad/s² ≈ 0.01745 rad/s².
Angular acceleration relates to torque through Newton's second law for rotation: τ = Iα, where τ is torque (N·m), I is moment of inertia (kg·m²), and α is angular acceleration (rad/s²). This is critical in motor control systems, gyroscopes, robotic joints, and vehicle stability systems. A washing machine drum spinning up from 0 to 1200 rpm in 10 seconds has an angular acceleration of 12.57 rad/s² or 720°/s².
| From | To rad/s² | Multiply by |
|---|---|---|
| 1 deg/s² | rad/s² | 0.017453 |
| 1 rev/s² | rad/s² | 6.28318 |
| 1 rpm/s | rad/s² | 0.10472 |
| 1 rad/s² | deg/s² | 57.2958 |
Angular acceleration measures the rate at which angular velocity changes over time. The SI unit is radians per second squared (rad/s²). When a motor spins up from rest to 3000 RPM in 2 seconds, the angular acceleration determines the torque required and the stress imposed on shaft couplings and bearings. Other common units include revolutions per minute per second (RPM/s), degrees per second squared (°/s²), and revolutions per second squared (rev/s²). Engineers use angular acceleration when designing flywheels, calculating start-up torque for motors, analyzing vehicle drivetrains, and designing robotics joint actuators. The relationship between angular acceleration (α), torque (τ), and moment of inertia (I) is τ = Iα, the rotational analog of Newton's second law F = ma. A high moment of inertia (heavy, large-radius wheel) requires a proportionally larger torque to achieve a given angular acceleration, which is why large industrial motors need high starting current to spool up heavy loads.
| Unit | rad/s² equivalent |
|---|---|
| 1 rev/s² | 6.2832 rad/s² |
| 1 RPM/s | 0.10472 rad/s² |
| 1 °/s² | 0.017453 rad/s² |
