In physics, **angular momentum** is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it.

**Continuum mechanics** is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

In physics, a **force** is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newton (N). Force is represented by the symbol **F**.

In physics, 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. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time.

In Newtonian mechanics, **momentum** is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If *m* is an object's mass and **v** is its velocity, then the object's momentum **p** is :

In physics, **motion** is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without reference to its cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.

In physics, a **conservative force** is a force with the property that the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done by a conservative force is zero.

In fluid dynamics, **Bernoulli's principle** states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book *Hydrodynamica* in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived **Bernoulli's equation** in its usual form. The principle is only applicable for isentropic flows: when the effects of irreversible processes and non-adiabatic processes are small and can be neglected.

In physics, **equations of motion** are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.

In theoretical physics and mathematical physics, **analytical mechanics**, or **theoretical mechanics** is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is *vectorial mechanics*.

In the physical science of dynamics, **rigid-body dynamics** studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are *rigid* simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.

The word "mass" has two meanings in special relativity: *invariant mass* is an invariant quantity which is the same for all observers in all reference frames, while the **relativistic mass** is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to *rest energy*, while relativistic mass is equivalent to *relativistic energy*.

In classical mechanics, **areal velocity** is a pseudovector whose length equals the rate of change at which area is swept out by a particle as it moves along a curve. In the adjoining figure, suppose that a particle moves along the blue curve. At a certain time *t*, the particle is located at point *B*, and a short while later, at time *t* + Δ*t*, the particle has moved to point *C*. The region swept out by the particle is shaded in green in the figure, bounded by the line segments *AB* and *AC* and the curve along which the particle moves. The areal velocity magnitude is this region's area divided by the time interval Δ*t* in the limit that Δ*t* becomes vanishingly small. The vector direction is postulated normal to the plane containing the position and velocity vectors of the particle, following a convention known as the right hand rule.

In theoretical physics, the **pilot wave theory**, also known as **Bohmian mechanics**, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse, and the paradox of Schrödinger's cat. To solve these problems, the theory is inherently nonlocal.

In physics, the motion of an electrically charged particle such as an electron or ion in a plasma in a magnetic field can be treated as the superposition of a relatively fast circular motion around a point called the **guiding center** and a relatively slow **drift** of this point. The drift speeds may differ for various species depending on their charge states, masses, or temperatures, possibly resulting in electric currents or chemical separation.

In physics, a **force field** is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field , where is the force that a particle would feel if it were at the point .

**Hamiltonian fluid mechanics** is the application of Hamiltonian methods to fluid mechanics. Note that this formalism only applies to nondissipative fluids.

**Classical mechanics** is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).

In physics, **Lagrangian mechanics** is a formulation of classical mechanics founded on the stationary-action principle. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, *Mécanique analytique*.

The **balance of angular momentum** or **Euler's second law** in classical mechanics is a law of physics, stating that to alter the angular momentum of a body a torque must be applied to it.