Radian per second to Megahertz
rad/s
MHz
Conversion History
| Conversion | Reuse | Delete |
|---|---|---|
| No conversion history to show. | ||
Quick Reference Table (Radian per second to Megahertz)
| Radian per second (rad/s) | Megahertz (MHz) |
|---|---|
| 0.001 | 0.00000000015915494309 |
| 0.1 | 0.00000001591549430919 |
| 1 | 0.0000001591549430919 |
| 6.283 | 0.00000099997050744638 |
| 10 | 0.00000159154943091895 |
| 100 | 0.00001591549430918953 |
| 1,000 | 0.00015915494309189535 |
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.
About Megahertz (MHz)
A megahertz (MHz) equals one million hertz and covers FM radio, VHF/UHF television, and older CPU clock speeds. FM radio in most countries is allocated the 87.5–108 MHz band. Early home computers and microprocessors ran at 1–20 MHz; the original IBM PC used an 8088 at 4.77 MHz. Wi-Fi channels in the 2.4 GHz band have bandwidths of 20 or 40 MHz. Wireless standards including Bluetooth, Zigbee, and many cellular bands also operate in the low hundreds of megahertz up to a few gigahertz.
FM radio broadcasts between 87.5 and 108 MHz. The original IBM PC ran at 4.77 MHz. Many smartphone processors boost to over 3,000 MHz (3 GHz).
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.
Megahertz – Frequently Asked Questions
Why did the original IBM PC run at the oddly specific speed of 4.77 MHz?
IBM needed a clock that could derive both the CPU timing and the NTSC color-burst frequency (3.579545 MHz) for the built-in composite video output. Multiplying the color-burst frequency by 4/3 gave 4.77 MHz — a convenient compromise that let one crystal oscillator serve two purposes. The weird number was pure engineering pragmatism, not performance targeting.
What is the 433 MHz band and why do so many gadgets use it?
The 433.05–434.79 MHz range is an ISM (Industrial, Scientific, Medical) band that is license-free in most of Europe. Cheap remote-control key fobs, weather stations, garage door openers, and IoT sensors all crowd into it because you can legally transmit at low power without a radio license. In the US, the equivalent unlicensed band is 315 MHz, which is why European and American car key fobs are not interchangeable.
How does FM radio achieve better sound quality than AM at a higher MHz frequency?
AM encodes audio by varying the wave's amplitude, which is vulnerable to electrical interference (lightning, motors). FM varies the frequency instead, making it inherently noise-resistant. FM also has a wider channel bandwidth (200 kHz vs. AM's 10 kHz), allowing it to carry the full 20–15,000 Hz audio spectrum in stereo. The MHz carrier frequency itself isn't what improves quality — it's the modulation method and bandwidth.
What happened to the megahertz race in CPUs during the early 2000s?
Intel and AMD marketed processors by clock speed — 500 MHz, 1 GHz, 2 GHz — implying faster was always better. By 2004, Intel's Pentium 4 hit 3.8 GHz but ran so hot and consumed so much power that performance-per-watt cratered. The industry pivoted to multi-core designs: instead of one core at 4 GHz, you got two or four cores at 2 GHz each, doing more total work with less heat. Raw megahertz stopped being a useful buying metric.
Why is Bluetooth limited to the 2,400 MHz band?
Bluetooth operates in the 2.4 GHz ISM band (2,400–2,483.5 MHz), which is reserved globally for unlicensed use. This avoids the need for regulatory approval in each country. The trade-off is sharing the band with Wi-Fi, microwaves, and baby monitors. Bluetooth mitigates interference by hopping between 79 channels 1,600 times per second — if one frequency is jammed, it has already moved on.