mass distribution

(noun)

Describes the spatial distribution, and defines the center, of mass in an object.

Related Terms

Examples of mass distribution in the following topics:

  • Locating the Center of Mass

    • The center of mass is a statement of spatial arrangement of mass (i.e. distribution of mass within the system).
    • The position of COM is given a mathematical formulation which involves distribution of mass in space:
    • If the mass distribution is continuous with the density ρ(r) within a volume V, the position of COM is given as
    • If a continuous mass distribution has uniform density, which means ρ is constant, then the center of mass is the same as the center of the volume.
    • Identify the center of mass for an object with continuous mass distribution

  • Weight of the Earth

    • where $F$ is the force between the masses, $G$ is the gravitational constant, $m_1$ is the first mass, $m_2$ is the second mass and $r$ is the distance between the centers of the masses.
    • In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its center.
    • For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.
    • The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance $r_0$ from the center of the mass distribution:
    • The portion of the mass that is located at radii $rmass enclosed within a sphere of radius $r_0$ was concentrated at the center of the mass distribution (as noted above).

  • The Physical Pendulum

    • Gravity acts through the center of mass of the rigid body.
    • However, it is not independent of the mass distribution of the rigid body.
    • A change in shape, size, or mass distribution will change the moment of inertia.
    • An example showing how forces act through center of mass.
    • A rigid rod with uniform mass distribution hangs from a pivot point.

  • Gravitational Attraction of Spherical Bodies: A Uniform Sphere

    • When considering the gravitational force exerted on an object at a point inside or outside a uniform spherically symmetric object of radius $R$, there are two simple and distinct situations that must be examined: the case of a hollow spherical shell, and that of a solid sphere with uniformly distributed mass.
    • Only the mass of the sphere within the desired radius $M_{mass of the sphere inside $d$) is relevant, and can be considered as a point mass at the center of the sphere.
    • That is, the sphere's mass is uniformly distributed.)
    • As in the case of hollow spherical shells, the net gravitational force that a solid sphere of uniformly distributed mass $M$ exerts on a body outside of it, is the vector sum of the gravitational forces acted by each shell of the sphere on the outside object.
    • More generally, this result is true even if the mass $M$ is not uniformly distributed, but its density varies radially (as is the case for planets).

  • Moment of Inertia

    • The moment of inertia is a property of the distribution of mass in space that measures mass's resistance to rotational acceleration about one or more axes.
    • The moment of inertia I of an object can be defined as the sum of mr2 for all the point masses of which it is composed, where m is the mass and r is the distance of the mass from the center of mass.
    • Assuming that the hoop material is uniform, the hoop's moment of inertia can be found by summing up all the mass of the hoop and multiplying by the distance of that mass from the center of mass.
    • All of the mass m is at a distance r from the center.
    • The moment of inertia depends not only on the mass of an object, but also on its distribution of mass relative to the axis around which it rotates.

  • Center of Mass of the Human Body

    • The center of mass (COM) is an important physical concept—it is the point about which objects rotate.
    • The center of mass (COM) is an important physical concept.
    • It is the point on an object at which the weighted relative position of the distributed mass sums to zero—the point about which objects rotate.
    • The center of mass of the human body depends on the gender and the position of the limbs.
    • where M is mass of the subject.

  • Order to Disorder

    • As an example, suppose we mix equal masses of water originally at two different temperatures, say 20.0º C and 40.0º C.
    • Second, once the two masses of water are mixed, there is only one temperature—you cannot run a heat engine with them.
    • Rather than having two masses at different temperatures and with different distributions of molecular speeds, we now have a single mass with a uniform temperature.

  • Rotational Inertia

    • There are, in fact, precise rotational analogs to both force and mass.
    • To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force F on a point mass m that is at a distance r from a pivot point.
    • The quantity mr2 is called the rotational inertia or moment of inertia of a point mass m a distance r from the center of rotation.
    • Different shapes of objects have different rotational inertia which depend on the distribution of their mass.
    • Explain the relationship between the force, mass, radius, and angular acceleration

  • Atomic Theory of Matter

    • The first was the law of conservation of mass, formulated by Antoine Lavoisier in 1789, which states that the total mass in a chemical reaction remains constant (that is, the reactants have the same mass as the products).
    • Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.
    • Atoms can be broken down into smaller pieces, and atoms of a given element can vary in mass and other properties (see isotopes and ions).
    • This is an illustration of the helium atom, depicting the nucleus (pink) and the electron cloud distribution (black).

  • Mass

    • In theoretical physics, a mass generation mechanism is a theory which attempts to explain the origin of mass from the most fundamental laws of physics.
    • The physical property we are covering in this atom is called mass.
    • Weight is a different property of matter that, while related to mass, is not mass, but rather the amount of gravitational force acting on a given body of matter.
    • Mass is an intrinsic property that never changes.
    • The International System of Units (SI) measures mass in kilograms, or kg.