Angular Acceleration Calculator
Calculate angular acceleration from torque and moment of inertia, or from change in angular velocity over time.
Shows resulting angle rotated.
Angular Acceleration
Angular acceleration is the rate of change of angular velocity. Two ways to calculate it:
Method 1 — From torque: α = τ / I
Method 2 — From velocity change: α = Δω / Δt = (ω_final − ω_initial) / time
Where:
- α = Angular acceleration (rad/s²)
- τ = Torque applied (N·m)
- I = Moment of inertia (kg·m²)
- ω = Angular velocity (rad/s)
- t = Time (s)
Rotational kinematics equations (constant α, analogous to v = v₀ + at):
- ω_f = ω₀ + αt
- θ = ω₀t + ½αt²
- ω_f² = ω₀² + 2αθ
Analogy with linear motion:
| Linear | Rotational |
|---|---|
| F = ma | τ = Iα |
| a (m/s²) | α (rad/s²) |
| v (m/s) | ω (rad/s) |
| x (m) | θ (rad) |
| m (kg) | I (kg·m²) |
Practical example: An electric motor applies 50 N·m of torque to a flywheel with I = 2.5 kg·m². The angular acceleration is: α = 50 / 2.5 = 20 rad/s²
Starting from rest, after 3 seconds: ω = 20 × 3 = 60 rad/s ≈ 573 RPM θ = ½ × 20 × 9 = 90 radians ≈ 14.3 full revolutions