Angular Acceleration Calculator
Calculate angular acceleration from angular velocity, tangential acceleration, or torque
Angular Acceleration Calculator
Calculation Results
Formula Used: α = (ω₂ - ω₁) / t
Example Calculations
Spinning Wheel
Initial velocity: 0 rad/s (starts from rest)
Final velocity: 24 rad/s
Time: 8 s
Angular acceleration: α = (24 - 0) / 8 = 3 rad/s²
Car Wheel
1. Tangential acceleration: 2 m/s², Wheel radius: 0.3 m
2. Angular acceleration: α = a/R = 2/0.3 = 6.67 rad/s²
3. This corresponds to rapid acceleration
Angular Acceleration Formulas
Acceleration Types
Common Units
rad/s² - Standard SI unit
°/s² - Degrees per second squared
rev/s² - Revolutions per second squared
RPM/s - RPM per second
Understanding Angular Acceleration
What is Angular Acceleration?
Angular acceleration is the rate of change of angular velocity over time. It describes how quickly an object's rotational speed is changing. Just like linear acceleration describes changing velocity in straight-line motion, angular acceleration describes changing rotational motion.
Angular Acceleration Formula
- •α = (ω₂ - ω₁) / t - From angular velocity change
- •α: Angular acceleration (rad/s²)
- •ω₁, ω₂: Initial and final angular velocities
- •t: Time interval
Alternative Formulas
From Tangential Acceleration: α = a / R
From Torque: α = τ / I
Angular Displacement: θ = ω₁t + ½αt²
Key Relationships
- Positive α: Rotational speed increasing
- Negative α: Rotational speed decreasing (deceleration)
- Zero α: Constant angular velocity
- Tangential relationship: a = αR (at radius R)
Units and Conversions
- •rad/s²: Standard SI unit
- •°/s²: Degrees per second squared
- •rev/s²: Revolutions per second squared
- •Conversion: 1 rad/s² = 57.3 °/s²
Real-World Examples
- •Car Engine: Accelerating from idle to high RPM
- •Washing Machine: Spin cycle acceleration
- •Figure Skater: Pulling arms in to spin faster
- •Turbine: Starting up power generation