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Linear motion, also called rectilinear motion, [1] is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion , with constant velocity (zero acceleration ); and non-uniform linear motion , with variable velocity ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Linear motion – motion that follows a straight linear path, and whose displacement is exactly the same as its trajectory. [Also known as rectilinear motion] Reciprocal motion; Brownian motion – the random movement of very small particles; Circular motion; Rotatory motion – a motion about a fixed point. (e.g. Ferris wheel).
The precise design trades off straightness, lack of acceleration, and the proportion of the driving rotation that is spent in the linear portion of the full curve. [ 4 ] The example to the right spends over half of the cycle in the near-straight portion.
Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone: [Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path. [20]
All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity , or, equivalently, Newton's first law of motion holds.
Jean d'Alembert (1717–1783). D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert, and Italian-French mathematician Joseph Louis Lagrange.
a cm is the linear acceleration of the center of mass of the body, m is the mass of the body, α is the angular acceleration of the body, and; I is the moment of inertia of the body about its center of mass. See also Euler's equations (rigid body dynamics).