Properties Of A Plane Area
Strings (SiPjAjk) = S7P2A21 Base Sequence = 12735 String Sequence = 12735 - 2 - 21
Consider figure 124.1:
(a) Where is the centroid of the plane area?
(b) Write the general expression for the moment of inertia about the x axis
(c) Write the general expression for the moment of inertia about the y axis
(d) Write the general expression for the polar moment of inertia
(e) Write the general expression for the product of inertia
(f) Write the general expression for the radius of gyration with respect to the x axis
(g) Write the genaral expression for the radius of gyration with respect to the y axis
(h) Show that the polar moment of inertia is the sum of the moment of inertia about the x axis and the moment of inertia about the y axis.
S7P2A21 (Identity - Physical Properties).
Pj Problem of Interest is of type identity (physical properties).
(a) Centroid is at G, the intersection of the lines m and l.
(b) Moment of inertia about x = Ix = ∫dA(x2).
(c) Moment of inertia about y = Iy = ∫dA(y2).
(d) Polar Moment of inertia = Jz = ∫dA(r2).
Where r, is the distance from O to dA.
(e) Product of inertia = Hxy = ∫dA(xy).
(f) Radius of gyration = kx = √(Ix/Area)
(g) Radius of gyration = ky = √(Iy/Area)
(h) Ix + Iy = ∫dA(x2) + ∫dA(y2).
So, Ix + Iy = ∫dA[x2 + y2] = ∫dA(r2) = Jz.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Single Variable Functions
Ordinary Differential Equations (ODEs)
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
More Pj Problem Strings