Angular Velocity Calculator

Calculate the angular velocity of a rotating object.

Calculator

Enter Your Values

Enter the angular displacement in radians

Enter the time in seconds

Table of Contents

1 Angular Velocity Formula
2 How to Calculate
3 Units and Conversions
4 Practical Examples
Concept

Angular Velocity Formula

Angular velocity is the rate of change of angular displacement with respect to time.

Formula:
ω = θ / t

Where:

  • ω = Angular velocity (rad/s)
  • θ = Angular displacement (rad)
  • t = Time (s)
Steps

How to Calculate

To calculate angular velocity, follow these steps:

  1. 1
    Measure the angular displacement in radians
  2. 2
    Measure the time taken for the displacement
  3. 3
    Divide the angular displacement by the time
Advanced

Units and Conversions

Common units for angular velocity include:

  • rad/s (radians per second)
  • rpm (revolutions per minute)
  • deg/s (degrees per second)
Common Conversions:
  • 1 rad/s = 9.549 rpm
  • 1 rad/s = 57.296 deg/s
  • 1 rpm = 0.1047 rad/s
Examples

Practical Examples

Example 1 Rotating Wheel

A wheel completes one full rotation (2π radians) in 2 seconds. Calculate its angular velocity.

θ = 2π rad

t = 2 s

ω = 2π / 2 = π rad/s ≈ 3.14 rad/s

Example 2 Earth's Rotation

Calculate the angular velocity of Earth's rotation (one full rotation in 24 hours).

θ = 2π rad

t = 24 × 3600 = 86400 s

ω = 2π / 86400 ≈ 7.27 × 10⁻⁵ rad/s

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