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Velocity and Acceleration

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Acceleration is a dynamic characteristic of an object, because according to Newton’s second law it essentially requires application of a force. A stationary position does not require an application of a force. A change in a position is associated with velocity and it does not require a force either, unless there is an opposing force, like friction. Acceleration always requires a force. In effect, position, velocity, and acceleration are all related – velocity is a first derivative of a position and acceleration is the second derivative. However, in a noisy environment, taking derivatives may result in extremely high errors, even if complex and sophisticated signal conditioning circuits are employed. Therefore, velocity and acceleration are not derived from the position detectors, but rather measured by special sensors. As a rule of thumb, in low-frequency applications (having a bandwidth on orders from 0 to 10 Hz), position and displacement measurements generally provide good accuracy. In the intermediate-frequency applications (less than 1 kHz), velocity measurement is usually favored. In measuring high-frequency motions with appreciable noise levels, acceleration measurement is preferred.


  • Ring Resonator
  • Spin Axis
  • Inertial Mass
  • Proof Mass
  • Velocity Sensor

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  • DOI: 10.1007/978-1-4419-6466-3_8
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  1. 1.

    d 2 y/dt 2 is the input acceleration of the accelerometer body.

  2. 2.

    These frequencies are chosen because they are removed from the power line frequencies and their harmonics.

  3. 3.

    Here we assume steady-state conditions and neglect radiative and convective heat transfers.

  4. 4.

    See Chap. 16 for a description of a Si diode as a temperature sensor.

  5. 5.

  6. 6.

    The Fredericks Company. PO Box 67, Huntingdon Valley, PA 19006.


  1. Articolo GA (1989) Shock impulse response of a force balance servo-accelerometer. In: Sensors Expo West proceedings, 1989. © Helmers Publishing, Inc.

    Google Scholar 

  2. (1991) Sensor signal conditioning: an IC designer’s perspective. Sensors, Nov. 23–30

    Google Scholar 

  3. Allen H, Terry S, De Bruin D (1989) Accelerometer system with self-testable features. Sens Actuators 20:153–161

    CrossRef  Google Scholar 

  4. Suminto JT (1991) A simple, high performance piezoresistive accelerometer. In: Transducers’91. 1991 international conference on solid-state sensors and actuators. Digest of Technical Papers. pp 104–107, ©IEEE

    Google Scholar 

  5. Haritsuka R, van Duyn DS, Otaredian T, de Vries P (1991) A novel accelerometer based on a silicon thermopile. In: Transducers’91. International conference on solid-state sensors and actuators. Digest of Technical Papers. pp 420–423, ©IEEE

    Google Scholar 

  6. Fox CHJ, Hardie DSW (1984) Vibratory gyroscopic sensors. In: Symposium gyro technology, DGON

    Google Scholar 

  7. Boxenhom BB, Dew B, Greiff P (1989) The micromechanical inertial guidance system and its applications. In: 14th biennial guidance test symposium, 6588th Test Group, Holloman AFB, New Mexico, 3–5 Oct 1989

    Google Scholar 

  8. Varnham MP, Hodgins D, Norris TS, Thomas HD (1991) Vibrating planar gyro. US Patent 5,226,321

    Google Scholar 

  9. Udd E (1991) Fiber optic sensors based on the Sagnac interferometer and passive ring resonator. In: Udd E (ed) Fiber optic sensors. Wiley, New York, pp 233–269

    Google Scholar 

  10. Ezekiel S, Arditty HJ (eds) (1982) Fiber-optic rotation sensors. Springer series in optical sciences, vol 32. Springer, New York

    Google Scholar 

  11. Fredericks RJ, Ulrich R (1984) Phase error bounds of fiber gyro with imperfect polarizer/depolarizer. Electron Lett 29:330

    Google Scholar 

  12. Bailleul G (1991) Vibracoax piezoelectric sensors for road traffic analysis. In: Sensor Expo proceedings, 1991. ©Helmers Publishing, Inc.

    Google Scholar 

  13. Radice PF (1991) Piezoelectric sensors and smart highways. In: Sensors Expo proceedings, 1991. Helmers Publishing, Inc.

    Google Scholar 

  14. Ebisawa M, Takeshi N, Tooru S (2007) Coaxial piezoelectric cable polarizer, polarizing method, defect detector, and defect detecting method. US Patent 7,199,508, 3 Apr 2007

    Google Scholar 

  15. Piezo film sensors technical manual. Measurement Specialties, Inc. April 1999

  16. Kato H, Kojima M, Gattoh M, Okumura Y, Morinaga S (1991) Photoelectric inclination sensor and its application to the measurement of the shapes of 3-D objects. IEEE Trans Instrum Meas 40(6):1021–1026

    Google Scholar 

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Correspondence to Jacob Fraden .

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Fraden, J. (2010). Velocity and Acceleration. In: Handbook of Modern Sensors. Springer, New York, NY.

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