⚙️ Angular Velocity Calculator
Calculate angular velocity
How to Use This Calculator
Enter Frequency
Input the frequency (f) in hertz (Hz). Frequency represents how many complete rotations or cycles occur per second. For example, if a wheel completes 5 full rotations per second, enter 5.
Calculate Angular Velocity
Click the "Calculate Angular Velocity" button to compute the result. The calculator will automatically convert your frequency to angular velocity in radians per second (rad/s) and also display the equivalent in revolutions per minute (RPM).
Review Results
Review the calculated angular velocity displayed in rad/s. The calculator also shows the RPM value for convenience. Use these values for your physics calculations, engineering applications, or rotational motion analysis.
Formula
ω = 2πf
Where:
• ω = Angular velocity (rad/s)
• f = Frequency (Hz)
• π ≈ 3.14159
RPM conversion: RPM = f × 60
Example 1: Rotating Wheel
A wheel rotates at 10 Hz. Calculate its angular velocity.
Given:
• Frequency (f) = 10 Hz
Solution:
ω = 2πf
ω = 2π × 10
ω = 20π
ω = 62.83 rad/s
RPM = 10 × 60 = 600 RPM
Example 2: Electric Motor
An electric motor runs at 60 Hz (standard AC frequency). What is its angular velocity?
Given:
• Frequency (f) = 60 Hz
Solution:
ω = 2πf
ω = 2π × 60
ω = 120π
ω = 377.0 rad/s
RPM = 60 × 60 = 3600 RPM
Frequently Asked Questions
What is angular velocity?
Angular velocity (ω) is the rate of change of angular displacement with respect to time. It measures how fast an object rotates around an axis and is measured in radians per second (rad/s). It's the rotational equivalent of linear velocity.
What's the difference between angular velocity and linear velocity?
Angular velocity (ω) describes rotational speed in rad/s, while linear velocity (v) describes translational speed in m/s. They're related by v = rω, where r is the radius. For example, a point on a wheel's rim has both angular velocity (how fast the wheel spins) and linear velocity (how fast the point moves through space).
How do I convert RPM to angular velocity?
First convert RPM to Hz: frequency (Hz) = RPM / 60. Then use ω = 2πf. For example, 1200 RPM = 20 Hz, so ω = 2π × 20 = 40π ≈ 125.66 rad/s.
Can angular velocity be negative?
Yes, angular velocity can be negative, indicating the direction of rotation. Positive typically means counterclockwise rotation, while negative means clockwise rotation. The sign depends on the coordinate system convention used.
What is the relationship between angular velocity and period?
The period (T) is the time for one complete rotation, and it's the reciprocal of frequency: T = 1/f. The relationship with angular velocity is: ω = 2π/T. Higher angular velocity means shorter period (faster rotation).
Where is angular velocity used in real-world applications?
Angular velocity is used in: calculating the speed of rotating machinery (motors, turbines, engines), analyzing planetary and satellite motion, designing gyroscopes and navigation systems, understanding wheel and gear systems, analyzing oscillatory motion, and in robotics for controlling joint rotations.
About Angular Velocity Calculator
The angular velocity calculator computes the rate of rotation in radians per second from frequency in hertz. Angular velocity is a fundamental concept in rotational kinematics, describing how fast an object rotates around an axis.
This calculator is essential for students studying rotational motion, engineers designing rotating systems, and anyone analyzing circular or oscillatory motion. It provides both angular velocity in rad/s and RPM for convenience, making it easy to work with different unit systems commonly used in physics and engineering.