Millihertz to Radian per second
mHz
rad/s
Conversion History
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Quick Reference Table (Millihertz to Radian per second)
| Millihertz (mHz) | Radian per second (rad/s) |
|---|---|
| 0.1 | 0.0006283185307179586 |
| 0.5 | 0.003141592653589793 |
| 1 | 0.006283185307179586 |
| 5 | 0.03141592653589793 |
| 10 | 0.06283185307179586 |
| 100 | 0.6283185307179586 |
| 500 | 3.141592653589793 |
About Millihertz (mHz)
A millihertz (mHz) is one thousandth of a hertz, corresponding to periods of minutes to hours. Millihertz frequencies appear in oceanography (tidal oscillations, slow wave action), geophysics (free oscillations of the Earth after major earthquakes), and physiology (very slow biological rhythms). The Earth's fundamental free oscillation modes — the lowest-frequency seismic normal modes — ring at a few millihertz in the aftermath of great earthquakes. Infrasound below 20 Hz also has a millihertz region for its slowest components.
Earth's gravest free oscillation mode rings at about 0.3 mHz (period ~54 minutes) after large earthquakes. A 1 mHz signal completes one cycle every 16.7 minutes.
About Radian per second (rad/s)
Radian per second (rad/s) is the SI unit of angular velocity, measuring how fast an angle changes over time. One full rotation (360°) equals 2π radians, so one revolution per second equals 2π rad/s ≈ 6.283 rad/s. Radian per second is the preferred unit in physics and engineering for rotational dynamics, since it makes equations involving centripetal acceleration and torque work cleanly without conversion factors. Electric motors, gyroscopes, and spinning spacecraft components are analyzed using rad/s.
Earth rotates at about 7.27 × 10⁻⁵ rad/s. A wheel spinning at 10 rad/s makes about 1.6 revolutions per second. A gyroscope precessing at 1 rad/s completes one full precession cycle in about 6.3 seconds.
Millihertz – Frequently Asked Questions
What does Earth sound like when it rings at millihertz frequencies after an earthquake?
After a magnitude-9 earthquake the entire planet vibrates like a struck gong, with its deepest mode at about 0.3 mHz — one oscillation every 54 minutes. The surface rises and falls by fractions of a millimeter. You cannot hear it (human hearing starts at 20 Hz), but gravimeters and seismometers worldwide pick it up. The 2004 Sumatra quake kept Earth ringing measurably for weeks.
Why do ocean scientists care about millihertz frequencies?
Ocean swells, tidal constituents, and seiches (standing waves in harbours or lakes) all oscillate in the millihertz band. A 10-second ocean swell is 100 mHz; a harbour seiche with a 10-minute period is about 1.7 mHz. Monitoring these frequencies helps coastal engineers predict resonance in ports and design breakwaters that don't amplify destructive wave energy.
Can humans sense anything at millihertz frequencies?
Not directly — our senses are far too fast. But some physiological rhythms operate here: the Mayer wave, a ~0.1 Hz oscillation in blood pressure, sits at the high end of the millihertz scale, and slower vasomotion (tiny blood vessel contractions) can dip below 10 mHz. You don't feel them as vibrations, but they show up clearly on a continuous blood-pressure monitor.
What is infrasound and does it overlap with millihertz?
Infrasound is sound below the ~20 Hz threshold of human hearing. The lowest infrasound blends into the millihertz range — the International Monitoring System for nuclear-test detection listens down to about 20 mHz. Sources include volcanic eruptions, meteor airbursts, severe storms, and ocean microbaroms (standing pressure waves between ocean swells and the atmosphere).
How are millihertz signals detected if they are too slow to hear?
Instruments record a time series (pressure, acceleration, displacement) over hours or days, then apply a Fourier transform to extract frequency content. Superconducting gravimeters can resolve Earth's free oscillations below 1 mHz by measuring gravity changes of 10⁻¹² g. The trick is not a fast sensor but a patient, ultra-stable one and enough data to separate signal from drift.
Radian per second – Frequently Asked Questions
Why do physics equations use radians per second instead of RPM or degrees?
Because radians make the maths clean. The formulas for centripetal acceleration (a = ω²r), angular momentum (L = Iω), and torque (τ = Iα) all assume ω is in rad/s. If you plug in RPM or degrees, you have to insert conversion factors of 2π/60 or π/180 everywhere. Radians are dimensionless ratios (arc length ÷ radius), so they vanish naturally from equations — no extra constants needed.
How fast does Earth rotate in radians per second?
Earth completes one full rotation (2π radians) in about 86,164 seconds (a sidereal day, slightly shorter than 24 hours). That gives approximately 7.292 × 10⁻⁵ rad/s. It sounds tiny, but at the equator it translates to a surface speed of about 465 m/s (1,674 km/h). You are always moving that fast — you just do not feel it because everything around you moves with you.
What is the difference between angular velocity and angular frequency?
They are the same number in rad/s but describe different things. Angular velocity refers to physical rotation — a wheel spinning. Angular frequency (often written ω = 2πf) describes oscillation — a vibrating spring or alternating current. A 60 Hz AC signal has ω ≈ 377 rad/s even though nothing is literally spinning. The distinction is conceptual, not mathematical.
How do you convert between rad/s and RPM?
Multiply rad/s by 60/(2π) ≈ 9.5493 to get RPM. Or divide RPM by the same factor to get rad/s. Quick shortcut: 1 rad/s ≈ 9.55 RPM, and 1,000 RPM ≈ 104.7 rad/s. If a motor spec says 3,600 RPM (common for a synchronous motor on 60 Hz mains), that is 3,600 ÷ 9.5493 ≈ 377 rad/s — the same ω as the mains frequency times 2π.
What angular velocity in rad/s does a figure skater reach during a spin?
An elite figure skater in a scratch spin pulls their arms in and reaches roughly 25–40 rad/s (about 4–6 revolutions per second). That is 240–360 RPM. The current record-holders approach 342 RPM (~35.8 rad/s). The speed increase when pulling arms in is a textbook demonstration of conservation of angular momentum — reducing the moment of inertia forces ω to increase.