Moment Of Inertia Statics
In some cases r is referred to as d for distance from the axis of rotation and in others as with the rod in the previous section it s replaced by length l. Lesson 69 parallel axis theorem example moment of inertia duration.
Area Moment Of Inertia S B A Invent
In american customary units we calculate stress in pounds per square inch psi so it is the common practice to use areas and derived properties measured in inches.
Moment of inertia statics. The unit of moment of inertia is a composite unit of measure. For example the moment of inertia can be used to calculate angular momentum and angular energy. 50 videos play all mix statics simple moment of inertia by composites youtube statics.
The application of newton s second law to a system gives. C4 4 moment of inertia. It must be specified with respect to a chosen axis of rotation.
What is a moment of inertia. In statics and solid mechanics the geometrical or area moment of inertia is of more interest. Jeff hanson 92 308 views.
Where bold font indicates a vector that has magnitude and direction. In the international system si m is expressed in kilograms and r in metres with i moment of inertia having the dimension kilogram metre square. The formula is given as follows.
Statics is the branch of mechanics that is concerned with the analysis of loads force and torque or moment acting on physical systems that do not experience an acceleration a 0 but rather are in static equilibrium with their environment. The moment of inertia otherwise known as the mass moment of inertia angular mass or rotational inertia of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis. Statics the moment of inertia can be defined as the second moment about an axis and is usually designated the symbol i.
It is a measure of an object s resistance to changes to its rotation. The moment of inertia is very useful in solving a number of problems in mechanics. Similar to how mass determines the force needed for a desired acceleration.
Since in dynamics there is no such concept as the inertia of an area the moment of inertia has no physical meaning. It depends on the body s mass distribution and the axis chosen with larger moments requiring more torque to change the body s rate of rotation. Equations for moment of inertia so a body s moment of inertia depends on its mass m its radius r and its axis of rotation.
Moment of inertia is not a physical quantity such as velocity acceleration or force but it enables ease of calculation. Customary system m is in slugs 1 slug 32 2 pounds and r in feet with i expressed in terms of slug foot square. Conveniently most american drawings have areas dimensioned in inches.
Also defined as the capacity of a cross section to resist bending. Moments of inertia of areas are used extensively in strength to calculate stresses and deflections in beams. It is a function of the geometry of the area.
Just a heads up although moment of inertia moi won t be used much in this statics course it is included because it s part of the statics course syllabus that is followed by almost all universities across the world.
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