Angular Acceleration Calculator

Calculate angular acceleration from angular velocity, tangential acceleration, or torque

Angular Acceleration Calculator

rad/s
rad/s
s

Calculation Results

0
Angular Acceleration (rad/s²)
No Acceleration
Acceleration Type
0
Initial ω (rad/s)
0
Final ω (rad/s)
0
Time (s)
0
Displacement (rad)

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

From Angular Velocity
α = (ω₂ - ω₁) / t
From Tangential Acceleration
α = a / R
From Torque
α = τ / I
Angular Displacement
θ = ω₁t + ½αt²

Acceleration Types

No Accelerationα = 0
Very Slow< 0.1 rad/s²
Slow0.1-1 rad/s²
Moderate1-10 rad/s²
Fast10-100 rad/s²
Very Fast> 100 rad/s²

Common Units

🔄

rad/s² - Standard SI unit

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°/s² - Degrees per second squared

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rev/s² - Revolutions per second squared

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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