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What is the product moments of inertia of plane area about its own centroidal axis?
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State ane prove perpendicular axis theorem?
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:DerivationWorking in Cartesian co-ordinates, the moment of inertia of the planar body about the axis is given by[2]: On the plane, , so these two terms are the moments of inertia about the and axes respectively, giving the perpendicular axis theorem.
State and prove perpendicular axis and parallel axis theorem?
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:
What are structural steel members?
Structural steel members are the I-beams which consist second moments of area (moment of inertia of plane area), it allow them to be very stiff in respect to their cross-sectional area.
Why can't a car plane or bicycle stop immediately?
inertia
What is the moment of inertia of a circular disk rotating about an axis if the mass is m and radius is r?
The answer will depend on whether the axis isthrough the centre of the disk and perpendicular to its plane,a diameter of the disk, orsome other axis.Unless that information is provided, the answer is meaningless.
Why the cross product of two vectors in plane is directed perpendicular to the plane?
because that is the def. of a cross-product!
How does product travel?
By plane, boat or trucks....
How do you find out the moment of inertia of a plane area?
By integration. This means the plane is divided into small pieces, and the contribution of each individual piece to the moment of inertia is evaluated. There are mathematical methods to do this more or less easily - systematically, at least - for certain simple figures, and you can find the moment of inertial of many common figures published in lists.
What is the difference between Bending and Direct Stress?
-> when a structural body gets deviated from its original position or from its centroidal axis due to externally applied load,then it is termed as BENDING->DIRECT STRESS is the stress which act normal to the plane-> stress and bending are the two different things. stress produced by load per area & bending is the effect produced by load and stress.
Where is exulted in The Hatchet?
In the novel "Hatchet" by Gary Paulsen, the term "exulted" is not specifically mentioned. However, the protagonist, Brian Robeson, experiences moments of triumph and success as he learns to survive in the wilderness after a plane crash. These moments could be described as exultant.
What is physical interpretation of dot product?
it is physically the projection or shadow of a line on a plane...
These matrices represent the coordinates of two figures in the plane. Is the product of these matrices defined Answer yes or no?
no
