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To calculate the average linear mass density, ¯, of this one dimensional object, we can simply divide the total mass, , by the total length, : ¯ = If we describe the rod as having a varying mass (one that varies as a function of position along the length of the rod, ), we can write: = Each infinitesimal unit of mass, , is equal to the product ...
Area density can be calculated as: = or =, where ρ A is the average area density, m is the total mass of the object, A is the total area of the object, ρ is the average density, and l is the average thickness of the object.
In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ ( r → ) = d m / d V {\displaystyle \rho ({\vec {r}})=dm/dV} , where d V {\displaystyle dV} is an elementary ...
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
Its density is infinitely differentiable, indeed supersmooth of order 2. [21] Furthermore, the density of the standard normal distribution (i.e. = and =) also has the following properties: Its first derivative is ′ = ().
The number density (symbol: n or ρ N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density.
If a given particle is taken to be at the origin O, and if = / is the average number density of particles, then the local time-averaged density at a distance from O is (). This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.
Specific volume is the inverse of the density of a substance; therefore, careful consideration must be taken account when dealing with situations that involve gases. Small changes in temperature will have a noticeable effect on specific volumes. The average density of human blood is 1060 kg/m 3.