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Centripetal Force

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

Maximum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Minimum Velocity in Friction Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Horizontal Curve - Degree of curve

Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The ... more

Uniform Circular Motion position (Y - coordinate)

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more

Uniform Circular Motion position (X - coordinate)

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more

Langarian point (radius around M2 in the absense of M1)

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Horizontal Curve - Allowable radius

The allowable radius for a horizontal curve can then be determined by knowing the intended design velocity, the coefficient of friction, and the allowed ... more

Distance of L3 Langarian point

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Distance of L1 and L2 Langarian points(M2<<M1)

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Velocity in Frictionless Banked Turn

A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more

Electron's speed at any radius ( related to the energy level)

Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the “stationary ... more

Minimum railway curve radius

The minimum railway curve radius, the shortest allowable design radius for railway tracks under a particular set of conditions. It has an important bearing ... more

Cyclotron resonance frequency

A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path. The particles are held to ... more

Horizontal curve - Sight obstraction distance (S<L)

Horizontal curve – Sight Distance Properties (S<L)

Horizontal Curves are one of the two important transition elements in geometric ... more

Young - Laplace equation

In physics, the Young – Laplace equation, is a nonlinear partial differential equation that describes the capillary pressure difference sustained ... more

Horizontal curve - Sight obstraction distance (S>L)

Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve ... more

Desired radius of a curve

The equation for the desired radius of a curve, takes into account the factors of speed and superelevation (e). This equation can be algebraically ... more

Gaussian beam ( radius of curvature )

In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

Descartes' theorem ( internally tangent circle to three given kissing circles)

n geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic ... more

Radial acceleration in circular motion

Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a ... more

Precession - (Torque-induced - Classical Newtonian)

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Maximum contact pressure between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Force on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Angular Acceleration

Torque, moment, or moment of force is the tendency of a force to rotate an object about an axis, fulcrum, or pivot.
Moment of inertia is the mass ... more

Centripetal(Centrifugal) Acceleration

Acceleration, in physics, is the rate of change of velocity of an object. An object’s acceleration is the net result of any and all forces acting on ... more

Vertical Curve - Stopping Sight Distance

Sight distance is dependent on the type of curve used and the design speed. For crest curves, sight distance is limited by the curve itself, as the curve ... more

Lensmaker's equation

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more

Maximum Pressure on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

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