# Modulus

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Related to Modulus: elastic modulus

## modulus

1. Physics a coefficient expressing a specified property of a specified substance
2. Maths another name for the absolute value (sense 2) of a complex number
3. Maths the number by which a logarithm to one base is multiplied to give the corresponding logarithm to another base
4. Maths an integer that can be divided exactly into the difference between two other integers

## Modulus

a geometric parameter of gears. For cylindrical spur gears the modulus m is equal to the ratio of the diameter dp of the pitch circle to the number of teeth z or the ratio of the pitch t along the pitch circle to the number π: m = dp/z = t/π. For cylindrical helical gears a distinction is made among the transverse modulus ms = dp/z = ts/∊ the normal modulus ms = tn/∊ and the axial modulus ma= /ta/∊, where ts, tn, and ta are, respectively, the transverse, normal, and axial pitches along the pitch cylinder. The values of gear moduli are standardized, which is the basis for standardization of the other gear parameters (the geometric dimensions of gears are made proportional to the modulus) and gear-cutting tools.

## Modulus

(mathematics). (1) The modulus (or absolute value) of a complex number z = x + iy is the number r = (the root is taken with the plus sign). If a complex number z is represented in trigonometric form, z = r(cos ϕ + i sin ϕ), then the modulus is the real number r. The modulus may be geometrically interpreted in the following way. A complex number z = x + iy can be represented by a vector issuing from the origin of a rectangular coordinate system and ending at the point with coordinates (x, y). The length of this vector is the modulus of the complex number z.

(2) The modulus for converting from a logarithm system with base a to a logarithm system with base b is the number M = 1/logab. To obtain the logarithms of the numbers x to the base b, if the logarithms of these numbers are known to the base a, it is necessary to multiply the latter by the modulus: logb = M logax.

## modulus

[′mäj·ə·ləs]
(mathematics)
The modulus of a logarithm with a given base is the factor by which a logarithm with a second base must be multiplied to give the first logarithm.
References in periodicals archive ?
Sitka spruce, MDF, and Lauan plywood samples were tested to determine their Young's modulus and shear modulus values.
The only shortcoming of the apparent modulus measurements we have presented here is that they do not define the actual stress and strain at which the measurements are made.
The 3PB and nanoindentation tests are used to measure the Young's modulus of the coating and the differences in the results obtained by the two methods are analyzed with the aid of the microstructures.
For granular materials, the most significant parameter that influences modulus is the confining stress (Yoder and Witczak 1975).
Ozonolysis of soybean oil was done to study the effect of functionality on the modulus development during reactive foaming process.
Wang, Young's Modulus of Porous Materials, Part 1, Theoretical Derivation of Modulus-Porosity Correlation, J.
DMA isothermal tests give the storage modulus, loss modulus and tan [delta] as a function of prolonged time at a constant temperature level.
For example, multiple deep indentations on a reference sample using oscillation superposed over the loading segment of each test yields multiple sets of modulus values as a function of penetration depth that can then be averaged and used either to check load-frame compliance or tip shape calibration.
Significance of Interface on the Modulus of Nanocomposites
Also, given an array of modulus values within the casting, separate feeding areas within the casting must be recognized to determine how many risers are required and where they should be located.
Modulus as a function of temperature was correlated to composite structure following established ASTM dynamic mechanical protocols.
The new office will provide sales and support services for the entire Modulus Video line of products, including its ME1000 AVC standard definition (SD) encoder, MD1000 AVC SD decoder and the forthcoming ME6000 AVC high definition (HD) encoder.

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