The radius of curvature of a curve at a point M(x,y) is called the inverse of the curvature K of the curve at this point: R=1K. Hence for plane curves given by the explicit equation y=f(x), the radius of curvature at a point M(x,y) is given by the following expression: R=[1+(y′(x))2]32|y′′(x)|.

The radius is half the diameter, so use the formula r = D/2. This is identical to the method used for calculating the radius of a circle from its diameter. If you have a sphere with a diameter of 16 cm, find the radius by dividing 16/2 to get 8 cm. If the diameter is 42, then the radius is 21.

Call the diameter d, (d=2r where r is the radius of the sphere). Call the distance from the observer to the centre of the sphere D; measure or calculate D. tan θ = 2r/D from which, by substituting the determined values for tanθ and D, out pops the value for 2r (=d).

[′sfir·ə·kəl ′rād·ē·əs] (mathematics) For a circle on a sphere, the smaller of the spherical distances from one of the two poles of the circle to any point on the circle.

spherometer

It has been given that the radius of curvature for a convex lens is 40 cm, for each surface.

Curvature is a measurement of how sharply bent a curve is at a particular point. In geological terms, curvature is how fast dip changes. Sharp edges have high curvature, and lower curvature implies a smoother, softer edge.

The flexure formula gives the internal bending stress caused by an external moment on a beam or other bending member of homogeneous material. It is derived here for a rectangular beam but is valid for any shape.

Generally, deflection can be calculated by taking the double integral of the Bending Moment Equation, M(x) divided by EI (Young’s Modulus x Moment of Inertia).

Calculate BM: M = Fr (Perpendicular to the force) Bending moment is a torque applied to each side of the beam if it was cut in two – anywhere along its length. The hinge applies a clockwise (+) moment (torque) to the RHS, and a counter-clockwise (-) moment to the LHS.

SFD and BMD: The shear force diagram (SFD) and bending moment. diagram(BMD) of a beam shows the variation of shear. force and bending moment along the length of the beam. These diagrams are extremely useful while designing the.

If one end of the ruler is lying on the desk and is being held down, and then a force is applied to the other end of the ruler, it will cause the ruler to bend. The ruler will experience the greatest bending moment at the end where the force is applied.

Explanation: Moment is a product of force and perpendicular distance and the bending moment is the algebraic sum of moments taken away from the left or the right of the section hence the SI units of bending moment is same as the moment i.e kNm.

Physical quantities of shear stress are measured in force divided by area. In SI, the unit is the pascal (Pa) or newtons per square meter.

The unit for shear stress is the unit of load (or weight) divide by the unit of area; i.e. N/m^2 or Pa (Pascal) for the SI system and lbf/ft^2 for English system.

The most frequently used units of pressure are pascal (Pa), kilopascal (kPa), megapascal (MPa), psi (pound per square inch), torr (mmHg), atm (atmospheric pressure) and bar.