Where does moment collide?

In mechanics, the moment of a force is its turning effect about a point or axis: the product of the force and the perpendicular distance from the axis to the force's line of action, so the same push produces a larger moment the farther out it acts. The related moment of inertia measures how a body's mass is distributed about an axis, and so how strongly it resists angular acceleration. Kleppner and Kolenkow's An Introduction to Mechanics develops torque as the moment of a force and the moment of inertia as the rotational analogue of mass. The referent is a mechanical turning effect about an axis, measured in newton metres, not a summary of a distribution, a phenomenological instant, or the magnetic strength of a dipole.[1]

Unit

A force's turning effect about an axis, in newton metres (N·m)

Recovery means

Not applicable

Measured by

Computed as force times perpendicular lever arm, or measured with a torque wrench or dynamometer about a defined axis

In statistics, the moments of a distribution are the expected values of successive powers of a variable, and together they summarise its shape: the first raw moment is the mean, the second central moment is the variance, and the third and fourth standardised central moments describe skewness and kurtosis. Pearson's 1894 Contributions to the mathematical theory of evolution used moments to fit frequency curves, the origin of what is now called the method of moments. The referent is a set of summary integrals of a probability distribution, carrying the variable's units or dimensionless once standardised, not a turning effect in mechanics, an instant in lived time, or a magnetic dipole.[2]

Unit

The expected value of a power of a variable; the k-th moment summarises distributional shape

Recovery means

Not applicable

Measured by

Estimated from a sample as the average of the k-th powers of the observations, taken raw or about the mean

In phenomenology, a moment is the instant of lived time, the present now through which experience passes. Husserl's analysis of internal time-consciousness treats the now-point not as an isolated dot but as always shading into what has just passed and what is about to arrive, so the present moment carries a thickness rather than being a bare point. Husserl's On the Phenomenology of the Consciousness of Internal Time works this structure out in detail. The referent is the experienced present instant within the structure of time-consciousness, not a turning effect about an axis, a summary of a distribution, or a magnetic dipole.[3]

Unit

The experienced present instant in the flow of lived time

Recovery means

Not applicable

Measured by

Not measured by number; described through phenomenological analysis of how the now is retained and anticipated

In electromagnetism, the magnetic moment of a body or particle is the vector that fixes both the torque it feels in a magnetic field and the field it produces as a dipole: a current loop, a bar magnet, or an electron each has a magnetic moment whose size sets how strongly it couples to a field. Odom, Hanneke, D'Urso, and Gabrielse's 2006 measurement pinned the electron's magnetic moment to remarkable precision with a one-electron quantum cyclotron. The referent is a magnetic dipole strength, measured in ampere square metres or as a multiple of a magneton, not a mechanical turning effect, a moment of a distribution, or an instant of lived time.[4]

Unit

A magnetic dipole strength, in ampere square metres (A·m²) or in magnetons

Recovery means

Not applicable

Measured by

Found from the torque in a known field, or for a particle from its spin precession or from its cyclotron and spin frequencies