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[note 1] The mathematical description of motion, or kinematics, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates.
The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [ 13 ]: 1112. The force in the equation is not the force the object exerts.
The three-dimensional linear vector space R3 is a set of all radius vectors. The space R3 is endowed with a scalar product , . Time is a scalar which is the same in all space E3 and is denoted as t. The ordered set { t } is called a time axis. Motion (also path or trajectory) is a function r : Δ → R3 that maps a point in the interval Δ from ...
The shear is constant in absolute value: it is half the central load, P / 2. It changes sign in the middle of the beam. The bending moment varies linearly from one end, where it is 0, and the center where its absolute value is PL / 4, is where the risk of rupture is the most important.
The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s −1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector.
Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of referenceto an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while ...
Accelerations in special relativity (SR) follow, as in Newtonian Mechanics, by differentiation of velocity with respect to time. Because of the Lorentz transformation and time dilation, the concepts of time and distance become more complex, which also leads to more complex definitions of "acceleration". SR as the theory of flat Minkowski ...
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...