Angular Velocity Calculator
Calculate angular velocity (ω) using frequency, period, or linear velocity and radius.
Result
Formula Used
Where:
ω = angular velocity
f = frequency
Where:
ω = angular velocity
T = period
Where:
ω = angular velocity
v = linear velocity
r = radius
Understanding Angular Velocity
Angular velocity measures how quickly an object rotates or revolves relative to another point, typically the center of rotation. It’s a vector quantity with both magnitude and direction.
Key Points:
- Angular velocity is measured in radians per second (rad/s)
- 1 complete revolution (360°) equals 2π radians
- Positive values indicate counter-clockwise rotation
- Negative values indicate clockwise rotation
Practical Applications:
- Calculating rotational speed of engines and motors
- Analyzing circular motion in physics
- Designing mechanical systems with rotating parts
- Astronomy for calculating planetary rotation
Frequently Asked Questions
What is the difference between angular velocity and linear velocity?
Angular velocity describes rotational speed (how fast something spins), while linear velocity describes straight-line speed (how fast something moves from point A to point B). They’re related by the equation v = ωr, where v is linear velocity, ω is angular velocity, and r is the radius.
How do I convert RPM to angular velocity?
To convert revolutions per minute (RPM) to radians per second (rad/s): Multiply the RPM value by 2π (approximately 6.28318) and then divide by 60. The formula is: ω (rad/s) = RPM × 2π / 60.
Can angular velocity be negative?
Yes, angular velocity can be negative. The sign indicates the direction of rotation: positive values typically represent counter-clockwise rotation, while negative values represent clockwise rotation when viewed from a standard reference point.