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radians per second to gigahertz conversion

radians per second to gigahertz conversion table

radians per second (rad/s)gigahertz (GHz)
00
11.591549430919e-10
23.1830988618379e-10
34.7746482927569e-10
46.3661977236758e-10
57.9577471545948e-10
69.5492965855137e-10
71.1140846016433e-9
81.2732395447352e-9
91.4323944878271e-9
101.591549430919e-9
203.1830988618379e-9
304.7746482927569e-9
406.3661977236758e-9
507.9577471545948e-9
609.5492965855137e-9
701.1140846016433e-8
801.2732395447352e-8
901.4323944878271e-8
1001.591549430919e-8
10001.591549430919e-7

How to convert radians per second to gigahertz?

Radians per second (rad/s) is a unit of angular frequency, which describes how quickly something is rotating or oscillating. Gigahertz (GHz), on the other hand, is a unit of frequency that describes how many cycles occur per second and is often used in the context of electromagnetic waves, especially radio and microwave frequencies.

To convert from radians per second to gigahertz, we need to understand the relationship between these units:

  1. One cycle per second is equivalent to 2π2\pi radians per second.
  2. Gigahertz is equal to 10910^9 cycles per second (Hertz, Hz).

Let's break this down step by step with the conversion factor:

Conversion Process:

  1. Convert radians per second to cycles per second (Hertz): 1 rad/s×(1 cycle2π radians)=12π Hz 1 \text{ rad/s} \times \left(\frac{1 \text{ cycle}}{2\pi \text{ radians}}\right) = \frac{1}{2\pi} \text{ Hz}

  2. Convert Hertz to Gigahertz: 12π Hz×(1 GHz109 Hz)=12π×109 GHz \frac{1}{2\pi} \text{ Hz} \times \left(\frac{1 \text{ GHz}}{10^9 \text{ Hz}}\right) = \frac{1}{2\pi \times 10^9} \text{ GHz}

  3. Simplify the expression: 12π×109≈1.59×10−10 GHz \frac{1}{2\pi \times 10^9} \approx 1.59 \times 10^{-10} \text{ GHz}

So, 1 radian per second is approximately 1.59×10−101.59 \times 10^{-10} gigahertz.

Real-World Examples:

Here are some real-world quantities of radians per second and their context:

  1. Earth's Rotation:

    • The Earth rotates at approximately 7.27×10−57.27 \times 10^{-5} rad/s.
    • In Gigahertz: 7.27×10−5 rad/s≈1.16×10−14 GHz7.27 \times 10^{-5} \text{ rad/s} \approx 1.16 \times 10^{-14} \text{ GHz}.

  2. Typical Household Fan:

    • A typical household fan might spin at around 100 rad/s100 \text{ rad/s}.
    • In Gigahertz: 100 rad/s≈1.59×10−8 GHz100 \text{ rad/s} \approx 1.59 \times 10^{-8} \text{ GHz}.

  3. High-Speed Mixer:

    • A high-speed industrial mixer might operate at around 500 rad/s500 \text{ rad/s}.
    • In Gigahertz: 500 rad/s≈7.96×10−8 GHz500 \text{ rad/s} \approx 7.96 \times 10^{-8} \text{ GHz}.

  4. Hard Disk Drive (HDD) Spindle:

    • A typical HDD might have a rotational speed of 7200 RPM7200 \text{ RPM}, which is equivalent to approximately 753.6 rad/s753.6 \text{ rad/s}.
    • In Gigahertz: 753.6 rad/s≈1.20×10−7 GHz753.6 \text{ rad/s} \approx 1.20 \times 10^{-7} \text{ GHz}.

These examples illustrate the significant differences in frequency across various applications, highlighting the usefulness of understanding these conversions.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the gigahertz to other unit conversions.

What is radians per second?

The radians per second is a measurement used for defining angular velocity or rotational speed. This is the standard SI unit for measuring angular velocity. Unit of radians per second is rad/srad/s or rad∗s−1rad*s^{-1}.

1 rad∗s−1=1ω=3602πdeg∗s−1=12πHz=0.159155Hz1\ rad*s^{-1} = 1\omega = \frac{360}{2\pi} deg*s^{-1} = \frac{1}{2\pi} Hz = 0.159155 Hz

Wikipedia page for explanation on Radian per second

What is gigahertz?

Gigahertz (GHz) is a unit of measurement for frequency, used to express the number of cycles or oscillations per second in electronic systems.

In essence, it represents one billion (1,000,000,000) cycles or oscillations per second. To break it down further:

  • 1 Hertz (Hz) = 1 cycle per second
  • 1 Kilohertz (kHz) = 1,000 cycles per second
  • 1 Megahertz (MHz) = 1 million cycles per second
  • 1 Gigahertz (GHz) = 1 billion cycles per second

In the context of electronic devices, such as computers, smartphones, and radios, gigahertz refers to the clock speed or operating frequency of a processor or other component. For example:

  • A computer with a CPU running at 2.5 GHz can execute 2.5 billion instructions per second.
  • A radio transmitter that operates on a frequency of 100 MHz would transmit 100 million cycles per second.

In summary, gigahertz is a unit of measurement for frequency, representing one billion cycles or oscillations per second, and is commonly used to express the operating frequencies of electronic devices.

Complete radians per second conversion table

Enter # of radians per second
Convert 1 rad/s to other unitsResult
radians per second to millihertz (rad/s to mHz)159.1549430919
radians per second to hertz (rad/s to Hz)0.1591549430919
radians per second to kilohertz (rad/s to kHz)0.0001591549430919
radians per second to megahertz (rad/s to MHz)1.591549430919e-7
radians per second to gigahertz (rad/s to GHz)1.591549430919e-10
radians per second to terahertz (rad/s to THz)1.591549430919e-13
radians per second to rotations per minute (rad/s to rpm)9.5492965855137
radians per second to degrees per second (rad/s to deg/s)57.295779513082

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