Angular Frequency Calculator

Calculate angular frequency for rotating and oscillating objects with precise physics formulas

Calculate Angular Frequency

Number of oscillations per unit time

Time for one complete oscillation

Angular Frequency Results

0.0000
rad/s
0.0000
rad/s (SI unit)

Formula used: ω = 2πf = 2π/T

Calculation: ω = 2π × 0.0000 Hz = 0.0000 rad/s

Example Calculations

Rotating Wheel Example

Problem: A tire rotates 200 radians in 40 seconds

Given: Δθ = 200 rad, Δt = 40 s

Formula: ω = Δθ / Δt

Solution: ω = 200 rad / 40 s = 5 rad/s

Oscillating Pendulum Example

Problem: A pendulum oscillates with frequency 2 Hz

Given: f = 2 Hz

Formula: ω = 2πf

Solution: ω = 2π × 2 = 12.566 rad/s

Key Concepts

ω

Angular Frequency

Rate of change of angular displacement

SI unit: rad/s

f

Frequency

Number of oscillations per second

Unit: Hz (cycles per second)

T

Period

Time for one complete cycle

T = 1/f

Key Formulas

For Rotating Objects

ω = Δθ / Δt

For Oscillating Objects

ω = 2πf = 2π/T

Period-Frequency Relation

T = 1/f

Understanding Angular Frequency

What is Angular Frequency?

Angular frequency is a scalar physical quantity that measures how quickly an object rotates or oscillates with respect to time. It's usually denoted by the Greek letters Ω or ω and is measured in radians per second (rad/s) in the SI system.

Key Characteristics

  • Measures rotational or oscillatory motion
  • Related to frequency by a factor of 2π
  • SI unit is radians per second (rad/s)
  • Can also be expressed in RPM, deg/s, or Hz

Applications

  • Mechanical vibrations and oscillations
  • Electric circuits (AC analysis)
  • Rotating machinery analysis
  • Wave mechanics and acoustics
  • Pendulum and spring-mass systems

Relationship with Other Quantities

Angular velocity: ω = v/r (for circular motion)

Linear frequency: f = ω/(2π)

Period: T = 2π/ω

Angular displacement: θ = ωt (constant ω)