Angular Acceleration Calculator — Rotational Motion Calculator
Calculate angular acceleration, angular velocity change, or time using rotational kinematics equations. Essential for mechanical engineering, robotics, and rotational dynamics analysis. See also our Torque Calculator and Moment of Inertia Calculator.
How to Calculate Angular Acceleration
- Select what you want to calculate from the dropdown menu.
- Enter the known values in the input fields.
- Click Calculate to solve for the unknown variable.
- Results show values in both radians and degrees for reference.
Angular Acceleration Formula
Angular Acceleration:
α = (ωf - ω0) / t = Δω / t
Where:
α = Angular acceleration (rad/s²)
ωf = Final angular velocity (rad/s)
ω0 = Initial angular velocity (rad/s)
Δω = Change in angular velocity (rad/s)
t = Time (s)
Rotational kinematics equations:
ωf = ω0 + α × t
θ = ω0 × t + ½ × α × t²
ωf² = ω0² + 2 × α × θ
Unit conversions:
1 rad/s = 180/π °/s ≈ 57.3 °/s
1 rad/s = 30/π RPM ≈ 9.55 RPMExample Calculation
Problem: A wheel accelerates from rest to 10 rad/s in 2 seconds. Find the angular acceleration.
Given: ω0 = 0 rad/s, ωf = 10 rad/s, t = 2 s
Solution: α = (10 - 0) / 2 = 5 rad/s²
Answer: The angular acceleration is 5 rad/s² or 286.5 °/s².
Angular Acceleration Reference Table
| System/Application | Angular Acceleration | Typical Range |
|---|---|---|
| Car engine startup | 50-200 rad/s² | High acceleration |
| Electric motor | 10-100 rad/s² | Variable speed |
| Washing machine spin | 1-10 rad/s² | Gradual acceleration |
| Bicycle wheel | 0.1-5 rad/s² | Human powered |
| Gyroscope | 0.01-1 rad/s² | Precision control |
| Wind turbine | 0.001-0.1 rad/s² | Slow acceleration |
| Earth rotation | 7.3×10⁻⁵ rad/s² | Constant (no accel) |
| Centrifuge | 100-1000 rad/s² | Laboratory equipment |
Technical Details
Angular acceleration describes how quickly angular velocity changes with time. It's the rotational analog of linear acceleration. Positive values indicate increasing angular velocity, while negative values indicate deceleration. Angular acceleration is related to torque through Newton's second law for rotation: τ = I × α, where τ is torque and I is moment of inertia. The SI unit is radians per second squared (rad/s²). Angular acceleration is crucial in analyzing rotating machinery, vehicle dynamics, and robotic systems. It determines how quickly objects can change their rotational speed.
Frequently Asked Questions
What is angular acceleration?
Angular acceleration is the rate of change of angular velocity with respect to time. It measures how quickly an object's rotational speed increases or decreases.
How does angular acceleration relate to torque?
Angular acceleration is directly proportional to applied torque and inversely proportional to moment of inertia: α = τ/I. More torque produces higher acceleration; more inertia reduces acceleration.
What's the difference between angular and linear acceleration?
Angular acceleration describes rotational motion (rad/s²), while linear acceleration describes straight-line motion (m/s²). They're related by: a = α × r, where r is the radius.
Can angular acceleration be negative?
Yes, negative angular acceleration indicates deceleration (slowing down). The sign depends on the chosen positive direction of rotation and whether the object is speeding up or slowing down.
How do you convert between rad/s² and RPM/s?
To convert rad/s² to RPM/s: multiply by 30/π ≈ 9.55. To convert RPM/s to rad/s²: multiply by π/30 ≈ 0.105. These conversions help relate to common rotational speed units.