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The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, [1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between ...
The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's second moment of area about a parallel axis through the body's centroid, the area of the cross section, and the perpendicular distance (d) between the axes. ′ = +
Then the line is parallel to the axis of the parabola and has the equation = (+) / Proof: can be done (like the properties above) for the unit parabola y = x 2 {\displaystyle y=x^{2}} . Application: This property can be used to determine the direction of the axis of a parabola, if two points and their tangents are given.
By the principal axis theorem, the two eigenvectors of the matrix of the quadratic form of a central conic section (ellipse or hyperbola) are perpendicular (orthogonal to each other) and each is parallel to (in the same direction as) either the major or minor axis of the conic.
Parallel axis theorem; Pauthenier equation; Perpendicular axis theorem; Plastic limit theorems; Pokhozhaev's identity; Poppy-seed bagel theorem; S. Scallop theorem;
If b = 0, the line is a vertical line (that is a line parallel to the y-axis) of equation =, which is not the graph of a function of x. Similarly, if a ≠ 0, the line is the graph of a function of y, and, if a = 0, one has a horizontal line of equation =.
The equations defining the transformation in two dimensions, which rotates the xy axes counterclockwise through an angle into the x′y′ axes, are derived as follows. In the xy system, let the point P have polar coordinates ( r , α ) {\displaystyle (r,\alpha )} .
right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r from the axis. The total angular momentum (spin + orbital) is J.