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The angular displacement (symbol θ, ϑ, or φ) – also called angle of rotation, rotational displacement, or rotary displacement – of a physical body is the angle (in units of radians, degrees, turns, etc.) through which the body rotates (revolves or spins) around a centre or axis of rotation.
The animations below depict the motion of a simple (frictionless) pendulum with increasing amounts of initial displacement of the bob, or equivalently increasing initial velocity. The small graph above each pendulum is the corresponding phase plane diagram; the horizontal axis is displacement and the vertical axis is velocity. With a large ...
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
Each of these constants carries a physical meaning of the motion: A is the amplitude (maximum displacement from the equilibrium position), ω = 2πf is the angular frequency, and φ is the initial phase.
It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement). A longitudinal deformation (in the direction of the axis) is called elongation . The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of ...
θ is the angular displacement (measured in radians) from the equilibrium position. Just as in the linear case, this law shows that the torque is proportional to the angular displacement, and the negative sign indicates that the torque acts in a direction opposite to the angular displacement, providing a restoring force to bring the system back ...
The above development is a special case of general rotational motion. In the general case, angular displacement, angular velocity, angular acceleration, and torque are considered to be vectors. An angular displacement is considered to be a vector, pointing along the axis, of magnitude equal to that of .
The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.. In the simplest case of circular motion at radius , with position given by the angular displacement () from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: =.