ⓘ Rotational speed of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute, cycles per seco ..


ⓘ Rotational speed

Rotational speed of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute, cycles per second, radians per second, etc.

The symbol for rotational speed is ω cyc {\displaystyle \omega _{\text{cyc}}} the Greek lowercase letter "omega".

Tangential speed v, rotational speed ω cyc {\displaystyle \omega _{\text{cyc}}}, and radial distance r, are related by the following equation:

v = 2 π r ω cyc {\displaystyle v=2\pi r\omega _{\text{cyc}}} v = r ω rad {\displaystyle v=r\omega _{\text{rad}}}

An algebraic rearrangement of this equation allows us to solve for rotational speed:

ω cyc = v / 2 π r {\displaystyle \omega _{\text{cyc}}=v/2\pi r} ω rad = v / r {\displaystyle \omega _{\text{rad}}=v/r}

Thus, the tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. It is important to note that the direct proportionality of v to r is not valid for the planets, because the planets have different rotational speeds ω.

Rotational speed can measure, for example, how fast a motor is running. Rotational speed and angular speed are sometimes used as synonyms, but typically they are measured with a different unit. Angular speed, however, tells the change in angle per time unit, which is measured in radians per second in the SI system. Since there are 2π radians per cycle, or 360 degrees per cycle, we can convert angular speed to rotational speed by

ω cyc = ω rad / 2 π {\displaystyle \omega _{\text{cyc}}=\omega _{\text{rad}}/2\pi \,}


ω cyc = ω deg / 360 {\displaystyle \omega _{\text{cyc}}=\omega _{\text{deg}}/360\,}


  • ω rad {\displaystyle \omega _{\text{rad}}\,} is angular speed in radians per second
  • ω deg {\displaystyle \omega _{\text{deg}}\,} is angular speed in degrees per second
  • ω cyc {\displaystyle \omega _{\text{cyc}}\,} is rotational speed in cycles per second

For example, a stepper motor might turn exactly one complete revolution each second. Its angular speed is 360 degrees per second 360°/s, or 2π radians per second 2π rad/s, while the rotational speed is 60 rpm.

Rotational speed is not to be confused with tangential speed, despite some relation between the two concepts. Imagine a rotating merry-go-round. No matter how close or far you stand from the axis of rotation, your rotational speed will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.

  • rotation 2π radians exactly When a direction is assigned to rotational speed it is known as rotational velocity or angular velocity. Rotational velocity
  • Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational
  • Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion
  • constant - speed propeller is a variable - pitch aircraft propeller that automatically changes its blade pitch in order to maintain a chosen rotational speed The
  • planets Orbital period Poles of astronomical bodies Retrograde motion Rotational speed Synodic day Leap Seconds United States Naval Observatory. Useful
  • the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis. According to the International
  • Torque, moment, moment of force or turning effect is the rotational equivalent of linear force. The concept originated with the studies by Archimedes
  • self - curing resins in an unheated mould, but shares slow rotational speeds in common with rotational molding. Spin casting should not be confused with either
  • User - defined settings and the rotational input speed of the shaft determine the speed at which an electronic zero - speed switch trips. A small timing delay
  • projected rotational velocity. In fast rotating stars polarimetry offers a method of recovering the actual velocity rather than just the rotational velocity
  • side along the road. For a given surface speed the speed of this pair along the road the rotational speed RPM of their wheels large for the skater
  • orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed All rotating
  • reduces movement speed and acceleration rates, but at a cost of reduced seek performance. Rotational latency sometimes called rotational delay or just latency