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The moment of inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section. Spinning figure skaters can reduce their moment of inertia by pulling in their arms, allowing them to spin faster due to conservation of angular momentum.
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics , and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [ 1 ]
An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where
The first moment of area is based on the mathematical construct moments in metric spaces.It is a measure of the spatial distribution of a shape in relation to an axis. The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σad].
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
The moment of inertia of an object, symbolized by , is a measure of the object's resistance to changes to its rotation. The moment of inertia is measured in kilogram metre² (kg m 2). It depends on the object's mass: increasing the mass of an object increases the moment of inertia.
The kinetic energy of an object is equal to the work, force times displacement , needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest.
The second polar moment of area, also known (incorrectly, colloquially) as "polar moment of inertia" or even "moment of inertia", is a quantity used to describe resistance to torsional deformation (), in objects (or segments of an object) with an invariant cross-section and no significant warping or out-of-plane deformation. [1]