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What is the formula to convert angular velocity in revolution per second to linear velocity in meters per second?
alphonsio

The formula to convert angular velocity expressed in revolutions per seconde [ rpsrps ] to linear speed expressed in meters per second [ m.s1m.s^{-1} ] is given by:

v=2πrNv = 2\pi r \cdot N

v(m.s1)=2π×r×N(rps)v_{(m.s^{-1})} = 2 \pi \times r \times N_{(rps)}

v(m.s1)6.2831853.r.N(rps)v_{(m.s^{-1})} \approx 6.2831853. r .N_{(rps)}

where:

  • vv is the linear velocity expressed in meters per second ( m.s1m.s^{-1} )
  • NN is the angular velocity expressed in revolution per second ( rpsrps )
  • rr is the radius expressed in meters ( mm )

To convert angular velocity in revolutions per second (rev/s) to linear velocity in meters per second (m/s), you can use the following formula:

v=2πrNv = 2\pi r \cdot N

where:

  • vv is the linear velocity in meters per second (m/s).
  • rr is the radius of the circular path in meters (m).
  • NN is the angular velocity in revolutions per second (rev/s).
  • 2πr2\pi r represents the circumference of the circle.

Explanation:

  • The circumference of a circle is 2πr2\pi r.
  • If an object completes one revolution, it travels a distance equal to the circumference.
  • Therefore, if it completes NN revolutions in one second, the linear velocity vv is given by the distance traveled per second, which is 2πr×N2\pi r \times N.

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