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Angular displacement of a body is the Angle in Radian s through which a point or line has been rotated in a specified sense about a specified Axis . When an object rotates about its axis, the motion cannot simply be analyzed as a particle , since in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of an object, it becomes simplier to congider the body itself rigid. A body is generally considered rigid when the seperations between all the particles remains constant throughoutthe objects 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. Thus the rotation of a rigid body over a fixed axis is referred to as Rotational Motion . In the example illustrated to the right, a particle on object P 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'', ). In this particular example, the value of heta is changing, while the value of the radius remains the same. (In rectangular coordinates (x,y) both x and y are going to 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 is measured in Radians rather than degrees. This is because it provides a very simple relationship between distance traveled around the circle and the distance ''r'' from the centre. : For example if an object rotates 360 degrees around a circle radius ''r'' the angular displacement is given by the distance traveled the circumference which is Divided by the radius in: which easily simplifies to . Therefore 1 revolution is radians. |
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