Angular Displacement

Angular Displacement
    Consider a particle performing circular motion, along the circumference of the circle with centre O and radius r, in anticlockwise direction as shown in figure. When the particle moves from P to Q in a
short time interval ‘’, the angle traced by the radius vector at the centre of the circle is  and the arc length

Definition:
   The angle traced by the radius vector at the centre of the circle performing circular motion, is called angular displacement.
It is denoted by letter or. By definition of arc length
Arc length () = Radius vector (r)  X  angle traced by the radius vector


    It is measured in radian. It is a dimensionless quantity since it is the ratio of two similar quantities. It is a conditional vector. For infinitesimal values of angular displacement it is a true vector and for any finite values it is a scalar quantity, since it does not obey the commutative law of vector addition. The direction of angular displacement is perpendicular to the plane directed upwards or downward depending upon sense of rotation.
   When the particle describe the motion in anticlockwise direction, the direction of angular
Displacement is perpendicular the plane directed Upwards. When the motion of the particle is in a clockwise direction, the direction of angular displacement is directed in downward direction.
    Its direction is given by right hand rule or right handed screw rule.
Right hand rule:
    Imagine the axis of rotation is to be held in the right hand with fingers folded Around the axis and stretch out the thumb curled fingers describe the direction of motion of particle and the stretched out thumb gives direction of angular displacement.

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