 Rotating-accelerometer centripetal term

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.