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Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
Angle ω dt is the very small angle between the two velocities and tends to zero as dt → 0. Figure 3: (Left) Ball in a circular motion – rope provides centripetal force to keep the ball in a circle (Right) Rope is cut and the ball continues in a straight line with the velocity at the time of cutting the rope, in accord with Newton's law of ...
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
Angle between two circles If the radius ρ {\displaystyle \rho } of the circle centered at P {\displaystyle P} is different from Π ( P ) {\displaystyle {\sqrt {\Pi (P)}}} one gets the angle of intersection φ {\displaystyle \varphi } between the two circles applying the Law of cosines (see the diagram):
The previous case can be extended to cover the case where the measure of the inscribed angle is the difference between two inscribed angles as discussed in the first part of this proof. Given a circle whose center is point O, choose three points V, C, D on the circle. Draw lines VC and VD: angle ∠DVC is an inscribed angle.
The angle A (respectively, B and C) may be regarded either as the dihedral angle between the two planes that intersect the sphere at the vertex A, or, equivalently, as the angle between the tangents of the great circle arcs where they meet at the vertex. Angles are expressed in radians.
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle.
To find the angle of a rotation, once the axis of the rotation is known, select a vector v perpendicular to the axis. Then the angle of the rotation is the angle between v and Rv. A more direct method, however, is to simply calculate the trace: the sum of the diagonal elements of the rotation