Angular Velocity Converter
Our free signal & frequency converter handles angular velocity conversions. See tables, ratios, and examples for quick reference.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
omega(rad/s) = RPM x 2pi / 60 | deg/s = rad/s x 180/pi | f(Hz) = omega / 2pi
All angular velocity conversions use radians per second as the base unit. One revolution equals 2 pi radians. RPM converts by multiplying by 2 pi / 60. Degrees convert using the factor 180 / pi. Frequency in hertz equals revolutions per second, which is angular velocity divided by 2 pi.
Worked Examples
Example 1: Engine RPM to Rad/s
Problem:Convert a car engine running at 3000 RPM to rad/s and Hz.
Solution:rad/s = 3000 x 2 x pi / 60 = 3000 x 6.2832 / 60 = 314.159 rad/s\nHz (rps) = 3000 / 60 = 50 Hz\nPeriod = 1 / 50 = 0.02 seconds per revolution
Result:3000 RPM = 314.159 rad/s = 50 Hz
Example 2: Hard Drive Spin Speed
Problem:A hard drive spins at 7200 RPM. What is its angular velocity in degrees per second?
Solution:rad/s = 7200 x 2 x pi / 60 = 753.982 rad/s\ndeg/s = 753.982 x 180 / pi = 43,200 deg/s\nThis means the platters rotate 120 times per second.
Result:7200 RPM = 753.98 rad/s = 43,200 deg/s
Frequently Asked Questions
What is angular velocity and how is it measured?
Angular velocity measures how fast an object rotates or revolves around an axis, expressed as the angle covered per unit time. The SI unit is radians per second (rad/s), where one full revolution equals 2 pi radians (approximately 6.2832 rad). In engineering and everyday use, RPM (revolutions per minute) is more common. Angular velocity differs from linear velocity in that it describes rotation rather than straight-line motion. The relationship between them is v = omega times r, where v is linear velocity and r is the radius.
What is the relationship between angular velocity and frequency?
Angular velocity (omega) and frequency (f) are related by omega = 2 pi times f. Frequency in hertz equals revolutions per second. The period (T) is the reciprocal of frequency: T = 1/f = 2 pi / omega. For example, an object rotating at 10 Hz has an angular velocity of 62.83 rad/s and a period of 0.1 seconds. In signal processing, angular frequency (omega) is used extensively in Fourier analysis and is measured in radians per second.
How does angular velocity apply to real-world applications?
Angular velocity is critical in many fields. Car engines typically run at 1000-7000 RPM. Hard disk drives spin at 5400 or 7200 RPM. A washing machine spin cycle operates at 800-1600 RPM. The Earth rotates at approximately 0.00007272 rad/s (one revolution per 23 hours 56 minutes). In mechanical engineering, angular velocity determines gear ratios, centrifugal forces, and power transmission. In electronics, angular frequency describes AC current oscillation (50 or 60 Hz mains frequency equals 314.16 or 376.99 rad/s).
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy