Search Results
“mechanics”
205 items
Reduced Mass
The reduced mass is the \"effective\" inertial mass appearing in the two-body problem of Newtonian mechanics.
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Intrinsic Permeability
Permeability in fluid mechanics and the earth sciences is a measure of the ability of a porous material (often a rock or an unconsolidated material) to allow fluids to pass through it. Intrinsic permeability is permea...
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Cauchy Number
The Cauchy number is a dimensionless number in continuum mechanics used in the study of compressible flows.
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De Broglie Frequency by Kinetic Energy
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics.
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De Broglie Wavelength by Momentum
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics.
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De Broglie Frequency by Velocity
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics.
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De Broglie Wavelength by Velocity
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics.
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De Broglie Wavelength by Kinetic Energy
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics.
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De Broglie Frequency by Momentum
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics.
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De Broglie Angular Frequency by Velocity
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics.
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De Broglie Angular Frequency by Momentum
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics.
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Dean Number
The Dean number is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels.
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De Broglie Angular Frequency by Kinetic Energy
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics.
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Relativistic de Broglie Frequency by Velocity
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Wavelength by Velocity
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Wavelength by Kinetic Energy
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Frequency by Kinetic Energy
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Frequency by Momentum
The de Broglie frequency is the frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Wavelength by Momentum
The de Broglie wavelength is the wavelength associated with a massive particle in motion according to quantum mechanics accounting for relativistic effects.
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Pendulum
A simple pendulum is an isolated system that assumes a massless, inextensible and taut cord; a point mass weight at the end, with motion occurring only in two dimensions; no friction or air resistance; a uniform gravi...
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Relativistic de Broglie Angular Frequency by Momentum
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Relativistic de Broglie Angular Frequency by Velocity
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Reynolds Number Using Kinematic Viscosity
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.
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Relativistic de Broglie Angular Frequency by Kinetic Energy
The de Broglie angular frequency is the angular frequency associated with a massive particle in motion according to quantum mechanics, accounting for relativistic effects.
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Reynolds Number Using Dynamic Viscosity
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.
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Kepler's First Law
Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The first law states that the orbit of a planet is an ellipse with the Sun at one of the two foci.
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Mechanical Stress
Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other.
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Gravitational Acceleration
Gravitational acceleration is the acceleration on an object caused by the force of gravitation.
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Archimedes's Principle
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
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Velocity Components
The velocity of an object is the rate of change of its position with respect to a frame of reference. Its components are the portions of the velocity in the direction of the coordinate system vectors.
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Escape Velocity
The escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.
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Rolling Motion
Rolling is a type of motion that combines rotation (commonly of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exi...
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Work by Gravity
A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another or from one form to another.
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Kinetic Energy
The kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
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Force Components
The force components describe how the force is distrubuted along the x and y axes of a surface.
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Elastic Collision
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Perfectly elastic collisions...
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Weight on Other Bodies
The weight of an object is usually taken to be the force on the object due to the gravity of a body.
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Work by Force
A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another or from one form to another.
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Pressure Formula
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
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Work by Torque
A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another or from one form to another.
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Coriolis Effect
The Coriolis force is an inertial force that acts on objects that are in motion relative to a rotating reference frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the obj...
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Projectile Path
A projectile is any object thrown into space (empty or not) by the exertion of a force. The projectile path describes the trajectory of that projectile under the influence of gravity.
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Two Connected Springs in Serial
A spring is an elastic object used to store mechanical energy.
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Spring Harmonic Oscillator
A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement.
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Spring Constant for Helical Spring
The spring constant is the stiffness of a spring—the force needed to stretch it a certian distance.
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Damped Harmonic Oscillator
A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped harmonic oscillator experiences a frictional force (dampin...
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Ideal Rocket Equation
The ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity, and...
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Kepler's Third Law
Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The third law states that the square of the orbital period of a planet is proportional to the cube of the se...
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Work by Acceleration and Distance
A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another or from one form to another.
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Pendulum Harmonic Oscillator
A pendulum harmonic oscillator is a pendulum that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement.
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Work by Force at an Angle
A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. Work transfers energy from one place to another or from one form to another.
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Elastic Surface Collision
An elastic surface collision is an encounter between a particle and a surface in which the kinetic energy of the particle after the encounter is equal to the kinetic energy before the encounter. Perfectly elastic coll...
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Two Connected Springs in Parallel
A spring is an elastic object used to store mechanical energy.
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Elliptical Cylinder Mass
An elliptical cylinder is a cylinder whose cross-section is an ellipse.
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Speed under Constant Acceleration
The speed of an object is the magnitude of its velocity (the rate of change of its position).
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Maximum Spring Force
The maximum spring force is the maximum force the spring can exert before permanent deformation.
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Mechanical Stress for a Cylinder
The mechanical stress for a cylinder expresses the internal forces that neighboring particles within the cylinder exert on each other.
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Rolling Friction Coefficient
Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object or surface.
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Impulse for Constant Force
Impulse is the integral of a force, F, over the time interval, t, for which it acts.
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Circular Orbit Velocity
The circular orbit velocity describes the speed of an object in a stable orbit at a fixed distance around another body.
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Rotational Kinetic Energy
Rotational kinetic energy, or angular kinetic energy, is kinetic energy due to the rotation of an object and is part of its total kinetic energy.
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Parallel Axis Theorem
The parallel axis theorem can be used to determine the mass 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 ...
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Perfectly Inelastic Collision
An inelastic collision is a collision in which kinetic energy is not conserved due to the action of internal friction. A perfectly inelastic collision occurs when the maximum amount of kinetic energy of a system is lo...
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Small-Oscillation Pendulum
A simple pendulum is an isolated system that assumes a massless, inextensible and taut cord; a point mass weight at the end, with motion occurring only in two dimensions; no friction or air resistance; a uniform gravi...
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Relativistic Kinetic Energy
The kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
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Torsion Harmonic Oscillator
A torsion harmonic oscillator is a twisting system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement.
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Hohmann Angular Alignment
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The angular alignment is the bearing needed to make the transfer.
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Pressure of a Column of Fluid
The pressure of a column of fluid depends on the surface pressure and the depth of the column.
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Kinetic Friction Coefficient
Kinetic friction is the force resisting the relative motion of solid surfaces sliding against each other.
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Driven Harmonic Oscillator
A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A driven harmonic oscillator experiences an external time-dependent...
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Hooke's Law for Force
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance.
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Mechanical Advantage of a Lever
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case a lever.
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Projectile Slant Range
A projectile is any object thrown into space (empty or not) by the exertion of a force. The projectile slant range describes the final distance of that projectile under the influence of gravity along a nonhorizontal s...
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Elliptical Cylinder Volume
An elliptical cylinder is a cylinder whose cross-section is an ellipse.
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Gravitational Potential Energy
Gravitational potential energy is the energy of an object due to gravity near the surface of a gravitating body.
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Vis-Viva Equation
The vis-viva equation, also referred to as the orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical en...
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Newton's Second Law
In an inertial reference frame, the vector sum of the forces on an object is equal to the mass of that object multiplied by the acceleration of the object.
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Eckert Number
The Eckert number is a dimensionless number used in continuum mechanics. It expresses the relationship between a flow's kinetic energy and the boundary layer enthalpy difference, and is used to characterize heat dissi...
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Inclined Span Catenary Sag
The inclined span catenary sag describes the tensions and sagging curve, or catenary, of a cable connecting two points at different elevations.
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Mechanical Advantage of a Wedge by Dimensions
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case a wedge.
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Equation of Motion Using Distance
Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Hohmann Total Delta-V
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The total delta-v is the change in velocity needed to enter and exit the elliptical ...
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Damped Pendulum Harmonic Oscillator
A pendulum harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped pendulum harmonic oscillator experiences a fricti...
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Angular Momentum of a Rigid Body
Angular momentum is the rotational analog of linear momentum. For a rigid body, it equals the cross-product of the particle's position vector (relative to some origin) and its momentum vector.
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Hohmann Entrance Delta-V
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The entrance delta-v is the change in velocity needed to enter the elliptical orbit.
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Driven Torsion Harmonic Oscillator
A torsion harmonic oscillator is a twisting system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A driven torsion harmonic oscillator experiences a...
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Level Span Catenary Sag
The level span catenary sag describes the tensions and sagging curve, or catenary, of a cable connecting two points at the same elevation.
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Mechanical Advantage of a Pulley System
Mechanical advantage is a measure of the force amplification achieved by using a tool—in this case a pulley system.
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Driven Pendulum Harmonic Oscillator
A pendulum harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A driven pendulum harmonic oscillator experiences an exter...
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Damped Spring Harmonic Oscillator
A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped spring harmonic oscillator experiences a frictional...
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Power Exerted on a Rotating Object
Torque is a rotational force. Torque acting through a rotational distance over time creates power.
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Driven Spring Harmonic Oscillator
A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A driven spring harmonic oscillator experiences an external ...
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Newton's Law of Universal Gravitation
Newton's law of universal gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the s...
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Angular Velocity under Constant Angular Acceleration
The angular velocity of a body is the rate of change of its angular displacement with respect to time.
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Mechanical Advantage of a Wheel and Axle
Mechanical advantage is a measure of the force amplification achieved by using a tool—in this case, a wheel and axle.
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Damped Driven Harmonic Oscillator
A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, proportional to the displacement. A damped driven harmonic oscillator experiences a frictional force...
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Damped Torsion Harmonic Oscillator
A torsion harmonic oscillator is a twisting system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped torsion harmonic oscillator experiences a...
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Maximum Shear Stress in Spring
The maximum shear stress in a spring is the maximum shear stress the spring can suffer before permanent deformation.
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Hohmann Exit Delta-V
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The exit delta-v is the change in velocity needed to exit the elliptical orbit.
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Momentum Using Kinetic Energy
Momentum is the product of the mass and velocity of an object.
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Hooke's Law for Potential Energy
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance.
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Mechanical Advantage of a Wedge by Angle
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case a wedge.
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Weber Number
The Weber number is a dimensionless number in fluid mechanics that is often useful in analyzing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curve...
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Centripetal Force Using Rotation Speed
A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and toward the fixed point of the instantaneous center of curvature of the path.
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Gravitational Acceleration for a Uniform Density Sphere
Gravitational acceleration for a uniform density sphere is the acceleration on an object caused by the force of gravitation.
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Static Friction Coefficient Using Friction Force
Static friction is a force that opposes the relative lateral motion of two solid non-moving surfaces in contact.
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Centripetal Force Using Angular Velocity
A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and toward the fixed point of the instantaneous center of curvature of the path.
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Hohmann Transfer Time Using Radii
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The transfer time is the time it takes to complete the transit along the orbit.
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Earth Satellite Period in a Circular Orbit
A circular orbit is the orbit at a fixed distance around any point by an object rotating around a fixed axis. The orbital period is the time it takes the object to revolve around the point, in this case the planet Earth.
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Mechanical Stresses on a Thin-Walled Hoop
A cylinder stress is a stress distribution with rotational symmetry, one that remains unchanged if the stressed object is rotated about some fixed axis.
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Equation of Motion Using Angular Displacement
Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Damped Driven Pendulum Harmonic Oscillator
A pendulum harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped driven pendulum harmonic oscillator experiences a...
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Centripetal Acceleration Using Rotation Speed
Centripetal acceleration is the rate of change of velocity of an object with respect to time as it moves in a circular path.
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Gravitational Binding Energy of a Uniform Sphere
The gravitational binding energy is the minimum energy that must be added to a system for the system to cease being in a gravitationally bound state.
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Centripetal Acceleration Using Angular Velocity
Centripetal acceleration is the rate of change of velocity of an object with respect to time as it moves in a circular path.
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Minimum Power Required to Move Object
The minimum power required to move an object depends on the work done and the time it takes to complete the movement.
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Mechanical Advantage of an Inclined Plane by Slope
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case an inclined plane.
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Mechanical Advantage of an Inclined Plane by Dimensions
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case an inclined plane.
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Mechanical Advantage of a Screw Using Lead
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case a screw.
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Damped Driven Torsion Harmonic Oscillator
A torsion harmonic oscillator is a twisting system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped driven torsion harmonic oscillator experi...
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Damped Driven Spring Harmonic Oscillator
A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. A damped driven spring harmonic oscillator experiences a fri...
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Fermi Energy for Non-Interacting Fermions
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute ...
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Equation of Motion Using Final and Initial Angle
Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Elastic Collision in Two Dimensions Using Impact Parameter
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Perfectly elastic collisions...
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Mechanical Advantage of a Screw Using Lead Angle
Mechanical advantage is a measure of the force amplification achieved by using a tool, in this case a screw.
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Elastic Collision in Two Dimensions Using Incident Angle
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Perfectly elastic collisions...
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Equation of Motion Using Final and Initial Position
Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Equations of Motion for a Round Object on an Inclined Plane
The equations of motion for a round object on an inclined plane are the equations that describe the behavior of the object in terms of its motion as a function of time. An inclined plane is a flat supporting surface t...
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Hohmann Transfer Time Using Semimajor Axis
The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The transfer time is the time it takes to complete the transit along the orbit.
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Hydraulic Conductivity
Hydraulic conductivity is a property of vascular plants, soils and rocks that describes the ease with which a fluid (usually water) can move through pore spaces or fractures. It depends on the intrinsic permeability o...
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Boussinesq Number
The Boussinesq number is a dimensionless number representing the square root of the ratio of inertia force to gravitational force.
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Capillary Action
Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity.
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Manning Formula
The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, such as open-channel flow.
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Torricelli's Theorem
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an orifice to the height of fluid above the opening. The law states that the speed of eff...
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Angular Diameter
The angular diameter or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view.
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Engineering Strain
Strain is a measure of deformation representing the displacement between particles in the body relative to a reference length.
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Hydrostatic Pressure
Hydrostatic pressure describes the pressure in a fluid at rest, where all frictional and inertial stresses vanish.
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Fanno Flow
Fanno flow describes the adiabatic flow through a constant area duct where the effect of friction is considered.
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Poiseuille's Law
Poiseuille's law is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross-section.
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Static Friction Coefficient Using Critical Sliding Angle
Static friction is a force that opposes the relative lateral motion of two solid non-moving surfaces in contact.
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Equations of Motion for a Round Object on an Inclined Plane Using Slope
The equations of motion for a round object on an inclined plane are the equations that describe the behavior of the object in terms of its motion as a function of time. An inclined plane is a flat supporting surface t...
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Slant Range to Aircraft
Slant range is the line-of-sight distance between two points (in this case, one point is an aircraft) that are not at the same level relative to a specific datum.
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De Laval Nozzle
A de Laval nozzle is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a hot, pressurized gas passing through it to a higher supersonic speed in th...
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Blasius Displacement Thickness
A Blasius boundary layer describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate, which is held parallel to a constant unidirectional flow.
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Nozzle Air Velocity
The nozzle air velocity describes the speed of air flowing out of a nozzle under pressure. A nozzle is a device designed to control the direction or characteristics of a fluid flow (especially to increase velocity) as...
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Viscosity Conversion Formula
The kinematic viscosity is the ratio of the dynamic viscosity μ to the density of the fluid.
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Rossiter Coefficient and Frequency
The Rossiter coefficient is related to the Strouhal number, a dimensionless number describing oscillating flow mechanisms. The frequency is the frequency of vortex shedding.
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Heat Transfer Coefficient
The heat transfer coefficient is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat.
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Blasius Skin Friction
A Blasius boundary layer describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate, which is held parallel to a constant unidirectional flow. Skin friction is friction between the...
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Hazen–Williams Equation
The Hazen–Williams equation is an empirical relationship that relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction.
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Venturi Flow Rate
The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi flow rate is the volume flow of the fluid as it passes through that...
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Bernoulli's Energy Equation
Bernoulli's energy equation derives from Bernoulli's principle, which states that an increase in the speed of a fluid across a surface will result in a decrease of the force exerted (pressure) on that surface, or a de...
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Helmholtz Resonator Frequency
Helmholtz resonance is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle.
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Average Speed by Displacement
The speed of an object is the rate of change of its position.
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Flow Rate for Rectangular Pipes
The volumetric flow rate is the volume of fluid that passes per unit time.
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Bejan Number for Heat Transfer
The Bejan number is the dimensionless pressure drop along a channel of length L.
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Speed by Initial and Final Values
The speed of an object is the rate of change of its position.
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Rossiter Coefficient and Strouhal Number
The Rossiter coefficient is related to the Strouhal number, a dimensionless number describing oscillating flow mechanisms. The frequency is the frequency of vortex shedding.
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Blasius Boundary Layer Thickness
A Blasius boundary layer describes the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate, which is held parallel to a constant unidirectional flow.
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Flow Rate for Circular Pipes
The volumetric flow rate is the volume of fluid that passes per unit time.
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Colebrook–White Equation for Pipe Roughness
The Colebrook–White equation expresses the Darcy friction factor as a function of the Reynolds number and pipe relative roughness, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.
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Equation of Circular Motion under Constant Acceleration
The equation of circular motion describes an object moving under constant angular acceleration in a circular as a function of time.
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Speed of Sound in an Ideal Gas by Pressure
The speed of sound is the distance traveled per unit time by a sound wave as it propagates through an elastic medium.
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Water Hammer Pressure with Slow Closure
Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is forced to stop or change direction suddenly (momentum change). A...
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Water Hammer Pressure with Fast Closure
Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid, but sometimes also a gas) in motion is forced to stop or change direction suddenly (momentum change). ...
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Darcy's Law Using Pressure Difference
Darcy's law is an equation that describes the flow of a fluid through a porous medium.
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Constant Translational Acceleration in a Straight Line
Constant translational acceleration in a straight line describes the equation of motion of an object moving under constant acceleration along a straight line as a function of time.
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Drag Force on a Sphere for Stokes Flow
Stokes flow is a type of fluid flow where advective inertial forces are small compared with viscous forces.
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Darcy's Law Using Hydraulic Gradient
Darcy's law is an equation that describes the flow of a fluid through a porous medium.
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Boussinesq Approximation Parameter Using Fluid Densities
The Boussinesq approximation is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by the acceleration due to grav...
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Area Moment of Inertia of an Annulus about a Centroidal Axis
The second moment of area, also known as moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard to ...
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Area Moment of Inertia of a Disk about a Centroidal Axis
The second moment of area, also known as the moment of inertia of a plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with rega...
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Moment of Inertia of a Cone
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform solid cone, the moments of inertia are tak...
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Moment of Inertia of an Ellipsoid
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform solid ellipsoid, the moments of inertia ar...
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Moment of Inertia of a Cuboid
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform solid cuboid, the moment of inertia is tak...
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Moment of Inertia of a Sphere
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analogue to mass. For a uniform solid sphere, the moments of inertia are...
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Barometric Formula for Density
The barometric formula (also called the exponential atmosphere or isothermal atmosphere) is a formula used to model how the density of the air changes with altitude.
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Barometric Formula for Pressure
The barometric formula (also called the exponential atmosphere or isothermal atmosphere) is a formula used to model how the pressure of the air changes with altitude.
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Moment of Inertia of a Cylinder
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform solid cylinder, the moments of inertia are...
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Area Moment of Inertia of a Regular Pentagon about a Centroidal Axis
The second moment of area, also known as moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard to ...
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Speed of Sound in an Ideal Gas by Temperature and Molar Mass
The speed of sound is the distance traveled per unit time by a sound wave as it propagates through an elastic medium.
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Area Moment of Inertia of a Half-Disk about a Centroidal Axis
The second moment of area, also known as the moment of inertia of a plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with rega...
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Boussinesq Approximation Parameter Using Approximated Gravitational Acceleration
The Boussinesq approximation is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by the acceleration due to grav...
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Colebrook–White Equation for Darcy–Weisbach Friction Factor
The Colebrook–White equation expresses the Darcy friction factor as a function of the Reynolds number and pipe relative roughness, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.
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Area Moment of Inertia of a Filled Trapezoid about a Centroidal Axis
The second moment of area, also known as moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard to ...
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Speed of Sound in an Ideal Gas by Temperature and Mass of Molecule
The speed of sound is the distance traveled per unit time by a sound wave as it propagates through an elastic medium.
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Area Moment of Inertia of a Filled Triangle about a Centroidal Axis
The second moment of area, also known as moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard to ...
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Area Moment of Inertia of a Filled Rectangle about a Centroidal Axis
The second moment of area, also known as moment of inertia of a plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard t...
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Area Moment of Inertia of a Regular Hexagon about a Centroidal Axis
The second moment of area, also known as the moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard...
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Area Moment of Inertia of a Quarter Disk about a Centroidal Axis
The second moment of area, also known as moment of inertia of a plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard t...
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Average Angular Velocity by Displacement
The angular velocity of a rotating body is defined as the rate of change of angular displacement.
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Moment of Inertia of a Point Mass
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass.
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Moment of Inertia of an Elliptical Lamina
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform elliptical lamina, the moments of inertia ...
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Moment of Inertia of a Triangular Plate
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform triangular plate, the moments of inertia a...
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Moment of Inertia of a Thin Disk
The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a disk of infinitesimal thickness, the moments of in...
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Angular Velocity by Initial and Final Values
The angular velocity of a rotating body is defined as the rate of change of angular displacement.
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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Volume
The Bose–Einstein condensation temperature is the temperature at which a free Bose gas transitions to a Bose–Einstein condensate. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at w...
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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Pressure
The Bose–Einstein condensation temperature is the temperature at which a free Bose gas transitions to a Bose–Einstein condensate. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at w...
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Bose–Einstein Condensation Temperature for Noninteracting Bosons Using Number Density
The Bose–Einstein condensation temperature is the temperature at which a free Bose gas transitions to a Bose–Einstein condensate. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at w...