The measurement of angular velocity is essential for cars, planes, and spacecraft. Launching a satellite to going to mars, you need to measure the speed of an object's rotation.

    Below is your ultimate guide to understanding angular velocity, and how it's used in the real world. If conversions get tough, plug your values into the angular velocity conversion calculator.

    Using it can help you develop a stronger intuition of this concept and the world around us. Let's dive in!

    FREQUENTLY ASKED QUESTIONS


    What is angular velocity?

    Angular velocity is the measurement of how fast an object is rotating around a central axis point.

    The standard unit of angular velocity is rad/s (radians per second).

    The understanding of an object's angular velocity is only possible by understanding the principles of Newton's gravitational mechanics.

    Examples

    The Moon

    When thinking of planetary objects, the angular velocity of the moon is a measurement of how fast it rotates around the earth.

    The Earth

    The angular velocity of the earth is a measurement of how fast the earth is rotating around the sun.

    A Bicycle

    The angular velocity of a bicycle wheel is the measurement of how fast the outermost point of the wheel is rotating around the central axel.

    You

    The angular velocity of you is a measurement of how fast you are rotating around the earth's core.

    Our Galaxy

    Theoretically, the angular velocity of our galaxy is a measurement of how fast it's rotating around the central supermassive black hole of the universe. At the macro scale, the Milky Way rotates around a larger black hole.

    Atoms

    Even at the atomic scale, protons, neutrons, and electrons measure their speed of rotation around an atom.

    Summary

    You can measure everything in the universe in terms of angular velocity because everything in the universe is in a constant state of rotation around something else.

    We rotate around the earth's core, the earth rotates around the sun, and the sun rotates around the Milky Way Galaxy's central black hole.

    How do you calculate angular velocity?

    Angular velocity equals the final angle of the object minus the initial angle. The sum, over time, equals the change of the object's position through time.

      ω = (θf - θi) / t

    We express angles in radians, which relate to the radius of a circle. So, we express an angular velocity in radians per second.

    This is similar to miles per hour, but, a tire is not linear, it is circular - or angled.

    We use the radian-per-second metric, signified as the Greek omega sign, equally, to express electronic frequency.

    How do you convert angular velocity?

    There are many different units that can be used to express angular velocity, so the conversions can get quickly confusing. To get a better idea, take a look at our handy conversion table.

    We'll discuss two common conversions below.

    How To: Rad/s to Rpm

    If the RPM of the car wheel equals 1, the angular velocity or radians per second equals about 0.10472.

      1 rpm = 0.10472 rad/s

    Formula

      Rpm = rad/s · 0.10472

    Simply multiply your rad/s by the conversion factor above to get your rpm equivalent.

    How To: Rad/m to Rpm

    In terms of angles, one revolution per minute equals 360 degrees of rotation per minute. So, it takes about 6.3 radians to equal one full 360-degree revolution of the car tire.

      1 rpm = 6.3 rad/m

    Formula

      Rpm = rad/m · 6.3

    To convert to rev/m, just multiply your rad/m by 6.3.

    To check your work or try some other conversions, use our free angular velocity conversion calculator.

    How is angular velocity used in space flight?

    In order for the Apollo astronauts to reach the moon, NASA scientists measured and predicted angular velocity measurements of many objects.

    To figure out how to launch a rocket to the moon, measurements of the moon's rotational speed around the earth must be precise.

    Angular Velocity Of The Moon

    The angular velocity of the moon results from several forces. The earth holds the moon in a gravitational grip as it pulls the moon along its rotation around the sun.

    The gravitational force is responsible for keeping the moon in rotation with the earth. On earth, the gravitational force directs downward, towards the earth's central core.

    In space, since heavenly bodies are in a zero-gravity medium, the only calculation of resistance relates to another bodies gravity.

    So the angular velocity measurement of any heavenly body can be accurate and consistent.

    What Are Orbital Eccentricities?

    Eight of the nine planets in our solar system experience very few substantial orbital eccentricities, something that obstructs the gravitational forces of a circular orbit.

    Mercury is the only planet that has an eccentric orbit, which results from its close proximity to the sun's gravity.

    When in the planets innermost rotation, the sun's gravity acts as a slingshot. It changes the angular velocity of Mercury to the Sun, depending on when the measurement is taken.

    Angular Acceleration of a Spacecraft

    Studying the angular mechanics of airplane flight is not enough to get a human into outer space.

    A spacecraft, launched from earth, must accelerate to a greater velocity of force than that which earth's gravity exerts upon it.

    In order to free the ship from the earth's gravitational pull, an applied force must exceed the gravitational force.

    To do this, NASA and other private space organizations use a combination of liquid and solid fuel.

    By controlling the fuels combustion rate, a capsule of astronauts can be transported beyond the reach of gravity.

    Summary

    Too much acceleration would render a spaceship lost, drifting beyond the reach of earth's gravity.

    NASA constructed equations to carefully measure the orbital mechanics of space flight to determine the exact amount of angular acceleration that was necessary.

    With this information, the fuel consumption is calculated to provide the right amount of force.

    Final thoughts?

    Tried and true practice enables space organizations around the world to put objects and individuals into many types of orbit. These include geosynchronous, polar, sun-synchronous, and more.

    The measurement of an object's angular velocity enables scientists, researchers, probes, and telescopes to advance humans understanding of the Earth and the Universe.

    Sometimes this requires converting to other similar units.

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