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A rotating accelerometer is an accelerometer whose sensing axes rotate with a moving component, such as a gear shaft. It can measure motion close to its source, but its output combines the point's actual acceleration with a changing projection direction. Treating its channels as fixed laboratory axes can therefore change the interpretation of a gear vibration spectrum. A NASA transmission experiment mounted a microelectromechanical system sensor package on a pinion and compared it with stationary housing measurements.^[ref]

For a rigid shaft rotating in a plane, let its center have inertial acceleration ${\mathbf{a}}_O$. An attached point at radius $r$ haswhere ${\mathbf{e}}_r,{\mathbf{e}}_t$ rotate with the shaft. The radial contribution is the rotating-accelerometer centripetal term. At constant $\omega =100rad/s$ and $r=0.020\mathrm{m}$, its magnitude is $200m/{\mathrm{s}}^2$ even without vibration of the center. For the ideal specific force convention, the measured vector is ${\mathbf{a}}_P-\mathbf{g}$ projected onto each sensor axis, so gravitational acceleration can also produce a changing projection.

Suppose a laboratory acceleration $A\cos (2\pi f_{m}t)$ projects onto a sensor direction rotating at $f_r$. The product contains components at $f_m-f_r$ and $f_m+f_r$:This measurement geometry can produce modulation sidebands without a damaged tooth. The NASA radial channel showed1854 and2060Hz around a1957Hz mesh frequency with103Hz rotation. Paired tangential channels also allowed different motion contributions to be separated by sums and differences.^[ref] Correct interpretation therefore specifies mounting radius, orientation, measurement calibration and rotation timing, as well as sensor bandwidth.

The rotating-accelerometer centripetal term is the inward acceleration contribution $-r{\omega }^2$ at a sensor rigidly attached a distance $r$ from a rotation axis. With outward radial unit vector ${\mathbf{e}}_r$ and tangential vector ${\mathbf{e}}_t$, differentiating the rotating position givesIt is a real kinematic acceleration, rather than an electronic zero error. A rotating accelerometer measures the relevant projection of specific force, so center motion and gravitational acceleration must also be included when interpreting an actual channel. A primary rotating-sensor experiment explicitly separates radial and tangential measurement contributions.^[ref]

At $r=0.020\mathrm{m}$ and $\omega =100rad/s$, the radial contribution is $-200m/{\mathrm{s}}^2$. It is steady in the rotating radial coordinate even though its direction continuously turns in a laboratory frame. Reversing rotation preserves this term because $\omega$ is squared; the tangential term instead follows angular acceleration.

A rotating-accelerometer speed-ripple term remains when speed is not constant. If $\omega (t)={\omega }_0+\epsilon \cos \Omega t$, thenFor the preceding radius, ${\omega }_0=100rad/s$ and ripple amplitude $\epsilon =1rad/s$ give mean $-200.01m/{\mathrm{s}}^2$, fundamental ripple amplitude4m/s² and second-ripple amplitude0.01m/s². Subtracting a record's mean removes only the steady part. A spectral component can therefore arise from speed variation in this kinematic term, which should be checked against the measured rotation history before attributing it to another vibration source.