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Angular Velocity Formula:
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Angular velocity (ω) is a measure of the rate of rotation, describing how fast an object rotates or revolves relative to another point. It is measured in radians per second (rad/s) and represents the angular displacement per unit time.
The calculator uses the angular velocity formula:
Where:
Explanation: The formula calculates how many radians an object rotates through per second based on the time it takes to complete one full rotation (period).
Details: Angular velocity is crucial in physics and engineering for analyzing rotational motion, designing mechanical systems, understanding planetary motion, and applications in robotics, automotive engineering, and astronomy.
Tips: Enter the period in seconds (time for one complete rotation). The value must be greater than zero. The calculator will compute the angular velocity in radians per second.
Q1: What's the difference between angular velocity and linear velocity?
A: Angular velocity measures rotational speed (rad/s), while linear velocity measures straight-line speed (m/s). They are related by v = ωr, where r is the radius.
Q2: How is angular velocity related to frequency?
A: Angular velocity ω = 2πf, where f is frequency in hertz (Hz). Frequency is the reciprocal of period (f = 1/T).
Q3: What are typical angular velocity values?
A: Values vary widely - from very slow (e.g., Earth's rotation: 7.27×10⁻⁵ rad/s) to very fast (e.g., dental drill: up to 400,000 rad/s).
Q4: Can angular velocity be negative?
A: Yes, negative angular velocity indicates rotation in the opposite direction from the defined positive direction.
Q5: How is angular velocity measured in practice?
A: Using devices like tachometers, encoders, or gyroscopes, depending on the application and required precision.