Calculate angular velocity, rotational frequency, period, linear speed, or radius for circular motion using the relationships ω = 2πf = 2π/T = v/r.
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Angular velocity (ω)
6.2832 rad/s
ω (rad/s)
6.2832
Frequency (Hz)
1.0000
Period (s)
1.0000
RPM
60.00
Also in Physics
Science — Physics
Angular velocity (ω) describes how quickly an object rotates, measured in radians per second. It relates to rotational frequency (f in Hz), period (T), and — when a radius is given — to the linear speed of a point on the rotating object. These relationships are fundamental in motor engineering, orbital mechanics, and robotics.
Angular velocity relates to frequency by ω = 2πf, and to period by ω = 2π/T. The linear (tangential) speed of a point at radius r from the axis is v = ωr. A wheel of radius 0.3 m rotating at 1800 RPM has ω = 1800 × 2π/60 ≈ 188.5 rad/s and a rim speed of 188.5 × 0.3 ≈ 56.5 m/s (≈ 203 km/h).
RPM (revolutions per minute) is common in mechanical engineering. RPS (revolutions per second) and Hz are equivalent. Degrees per second appears in navigation and robotics. The SI unit rad/s is used in physics. To convert: 1 RPM = 2π/60 ≈ 0.1047 rad/s. The calculator accepts any of these units and provides all equivalent values in the result.
Frequently asked questions
Angular velocity is a vector quantity with both magnitude (angular speed) and direction (the axis of rotation, by the right-hand rule). Angular speed is the scalar magnitude — how fast the rotation is, regardless of direction. For most scalar calculations, angular speed in rad/s is what matters.
Centripetal acceleration a_c = ω²r = v²/r. For a point at radius 0.5 m with ω = 10 rad/s, centripetal acceleration = 100 × 0.5 = 50 m/s² (about 5.1 g). This acceleration always points toward the centre of rotation.
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