The time rate of change of velocity. Acceleration is a physics term that measures the rate of change of velocity per unit of time. Because velocity is a directed or vector quantity involving both magnitude and direction, a velocity may change by a change of magnitude (speed) or by a change of direction, or both. It follows that acceleration is also a directed, or vector, quantity (Fig. 1). See also: Acceleration analysis; Acceleration measurement; Accelerometer; Speed; Velocity

The technique of measuring the magnitude and direction of acceleration. Measurement of acceleration (see illustration) includes translational acceleration with tangential and radial components and angular acceleration. See also: Acceleration

A mechanical or electromechanical instrument that measures acceleration. The two general types of accelerometers measure either the components of translational acceleration or angular acceleration. See also: Acceleration measurement

Any one of a number of related integral quantities which serve as the basis for general formulations of the dynamics of both classical and quantum-mechanical systems. The term "action" has been associated with four quantities: the fundamental action S, for general paths of a dynamical system; the classical action S_C, for the actual path; the modified action S′, for paths restricted to a particular energy; and action variables, for periodic motions. See also: Classical mechanics; Motion; Quantum mechanics

The analog of linear momentum for rotational motion. A particle with mass m moving with velocity v has linear momentum p = mv (Note: This article follows the convention of using bold, non-italicized variables for vectors and using non-bold, italicized variables for scalars.) The angular momentum of the particle can be written as the vector cross-product of its position vector r, and its linear momentum, p:

(1)

An oscillator that does not obey Hooke's law. This law is an idealized expression that assumes that a system displaced from equilibrium responds with a restoring force whose magnitude is proportional to the displacement. The use of Hooke's law results in a linear equation of motion that fails to describe many properties of the real world. Nature demonstrates two fundamentally different forms of nonlinearity, which may be called elastic anharmonicity and damping anharmonicity. To understand their difference, and the nature of a harmonic oscillator, it is necessary to understand potential functions. See also: Harmonic motion; Harmonic oscillator; Hooke's law; Nonlinear physics

The branch of applied physics which deals with the motion of projectiles and the conditions governing their motion. Ballistics is, for practical purposes, subdivided into exterior and interior ballistics. Exterior ballistics begins at the instant a projectile leaves the muzzle of a gun barrel or the instant after impact (Fig. 1); interior ballistics, logically, deals with the events preceding this instant, that is, the events inside the gun barrel or the details of the impact that produces the motion. See also: Army armament; Physics

A variation in the intensity of a composite wave which is formed from two distinct waves with different frequencies. Beats were first observed in sound waves, such as those produced by two tuning forks with different frequencies. Beats also can be produced by other waves. They can occur in the motion of two pendulums of different lengths and have been observed among the different-frequency phonons in a crystal lattice. See also: Crystal structure; Pendulum

A fixed point in a body of matter through which the resultant force of gravitational attraction acts. The center of gravity is an imaginary point in any given body that is convenient when performing calculations and conducting mechanical studies regarding the body. The center of gravity may not be near an object's geometric center if the object's constituent matter is not evenly distributed; for example, a uniformly weighted ruler's center of gravity will align with its center point, while a sledgehammer's center of gravity will be nearer to the tool's heavy end (see Illustration). The concept of the center of gravity can be used in structural engineering to assist with the design of bridges and buildings, for instance, and in calculations involving celestial bodies interacting via the force of gravity. See also: Bridge; Gravity; Structural engineering

That point of a material object or a system of objects that moves as if all the external forces were acting on the entire mass of the object or the system of objects concentrated at that point. The motion of a material object or a system of objects can be described in terms of the translational motion of the center of mass and the rotational motion about the center of mass. See also: Rotational motion; Rigid-body dynamics