Abstract
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.
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Notes
- 1.
d 2 y/dt 2 is the input acceleration of the accelerometer body.
- 2.
These frequencies are chosen because they are removed from the power line frequencies and their harmonics.
- 3.
Here we assume steady-state conditions and neglect radiative and convective heat transfers.
- 4.
See Chap. 16 for a description of a Si diode as a temperature sensor.
- 5.
- 6.
The Fredericks Company. PO Box 67, Huntingdon Valley, PA 19006.
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Fraden, J. (2010). Velocity and Acceleration. In: Handbook of Modern Sensors. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6466-3_8
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