Linear velocity

The linear velocity . It is one whose direction is always tangent to the path of the rotating particle. This velocity has a direction perpendicular to the axis of rotation (that is, to the vector ω ) to the centripetal acceleration and the radius vector .


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  • 1 Denotation
  • 2 Equation
  • 3 Linear speed as vector
  • 4 Relationship between linear speed and angular velocity
  • 5 Linear velocity and radius as vectors
  • 6 Sources


It is denoted by the letter ( v ). In the International System of Units it is expressed in meters / second (m / s)


The linear velocity modulus expresses the arc length , l, that the body describes in the unit of time:

v = l / t

Linear speed as vector

In the MCU linear velocity and centripetal acceleration are perpendicular to each other. Linear velocity is represented tangent to the circular path, that is, perpendicular to the radial direction and the centripetal acceleration always directed towards the center.

In Uniform circular movement the linear velocity as vector varies in direction and sense, but not in module , this is because the path is curvilinear, to the change direction of speed change it as a vector, and then a centripetal acceleration arises .

Relationship between linear speed and angular velocity

Between the linear velocity , v, the radius R of the path and the angular velocity , ω, there is the following relationship:

v = ωR

Similarly, between linear speed and centripetal acceleration there is the following relationship:

a = v² / R


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