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
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
Angular Frequency
Rate of change of angular displacement
SI unit: rad/s
Frequency
Number of oscillations per second
Unit: Hz (cycles per second)
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)