The angular displacement (symbol θ, , or φ), also called angle of rotation or rotational 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. Angular displacement may be signed, indicating the sense of rotation (e.g., clockwise); it may also be greater (in absolute value) than a full turn. When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time. When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the body's motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible. In the example illustrated to the right (or above in some mobile versions), a particle or body P is at a fixed distance r from the origin, O, rotating counterclockwise. It becomes important to then represent the position of particle P in terms of its polar coordinates (r, θ). In this particular example, the value of θ is changing, while the value of the radius remains the same. (In rectangular coordinates (x, y) both x and y vary with time). As the particle moves along the circle, it travels an arc length s, which becomes related to the angular position through the relationship: Angular displacement may be expressed in radians or degrees. Using radians provides a very simple relationship between distance traveled around the circle (circular arc length) and the distance r from the centre (radius): For example, if a body rotates 360° around a circle of radius r, the angular displacement is given by the distance traveled around the circumference - which is 2πr - divided by the radius: which easily simplifies to: . Therefore, 1 revolution is radians.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related courses (5)
PHYS-101(en): General physics : mechanics (English)
Students will learn the principles of mechanics to enable a better understanding of physical phenomena, such as the kinematics and dyamics of point masses and solid bodies. Students will acquire the c
PHYS-101(f): General physics : mechanics
Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr
PHYS-100: Advanced physics I (mechanics)
La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant l
Show more
Related lectures (39)
Lagrange II: Compound Pendulum Analysis
Explores the dynamics of a compound pendulum, emphasizing inertia and energy analysis.
Differential Analysis Fluid Flow
Explores types of motion and deformation in fluid elements, velocity fields, rotation, vorticity, conservation of mass, and stream functions.
Simple Pendulum and Harmonic Oscillator
Explores the dynamics of a simple pendulum and harmonic oscillator, including Hooke's Law and equations of motion.
Show more
Related publications (32)

3D printed large amplitude torsional microactuators powered by ultrasound

Mahmut Selman Sakar, Mehdi Ali Gadiri, Junsun Hwang, Amit Yedidia Dolev

Here, we introduce a design, fabrication, and control methodology for large amplitude torsional microactuators powered by ultrasound. The microactuators are 3D printed from two polymers with drastically different elastic moduli as a monolithic compliant me ...
2024

Flexible surgical device with controllable stiffness

Charles Baur, Lennart Rubbert

The invention relates to a surgical device (10), comprising a tubular outer shaft (12,) and an inner element (14) having an elongated shape, the outer shaft comprising a distal (30a) and a proximal (30b) outer hinges, the inner element comprising an inner ...
2022

Buoyancy-driven convection of droplets on hot nonwetting surfaces

François Gallaire, Eunok Yim

The global linear stability of a water drop on hot nonwetting surfaces is studied. The droplet is assumed to have a static shape and the surface tension gradient is neglected. First, the nonlinear steady Boussinesq equation is solved to obtain the axisymme ...
AMER PHYSICAL SOC2021
Show more
Related concepts (7)
Angular velocity
In physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
Angular frequency
In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves). Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity. Angular frequency can be obtained multiplying rotational frequency, ν (or ordinary frequency, f) by a full turn (2π radians): ω=2π radν.
Turn (angle)
One turn (symbol tr or pla) is a unit of plane angle measurement equal to 2π radians, 360 degrees or 400 gradians. Thus it is the angular measure subtended by a complete circle at its center. Subdivisions of a turn include half-turns and quarter-turns, spanning a semicircle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r).
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.