Wednesday, May 15

Angular Displacement

We know that linear displacement of a body is the difference between final position and initial position of a body. When there is a rotational motion then the displacement is called angular displacement and is different from linear displacement. I like to share this formula for angular velocity with you all through my article.

Let us understand What is Angular Displacement?
It is the angle through which a body has been rotated about certain axis. In a rotational motion the velocity of the particle keeps on changing at every instant.
So rotational motion is dealt I a different way. In this case the body is considered as rigid instead of particle as the distance between all the particle remains constant throughout the motion.

Observe the diagram given above. The object starts moving from its initial position to point A. In such a case the distance of the object remains constant from origin throughout its motion.
The coordinates of the object is then defined in polar coordinate system as (r, Ө) where r is its distance from origin and Ө is the angle it has covered from x axis. Ө keeps on varying and r remains constant during the motion. As particle rotates along the circle it covers an arc on the circle which is given by:
S = r.Ө, here s is the arc covered by the object; r and Ө are radius and angle covered by the object.
Angular displacement is Ө and Angular Displacement Units are radians and is given by the following relation:
Ө = S/r
Example: if a body rotates an angle of 180 degree on a circle of radius r then angular-displacement is given by the distance travelled n circumference which is πr divided by the radius such as:
Ө = πr/r = π
If the object starts motion on the circle at some point other than on x axis which makes an angle Ө1 with x axis and then moves to other point which makes an angle Ө2 with x axis then angular displacement is given by the final angle minus initial angle i.e. Ө = Ө2 – Ө1.

Angular Velocity and Acceleration are other rotational terms. During the rotation even if the particle moves with a constant rotational speed the particle accelerates. This is due to the fact that it always changes its direction of movement. Angular acceleration is given as rate of change of angular velocity and is denoted by . Its unit is radians.second2.
= d^2Ө/dt^2
= dω/dt. Here ω is angular velocity. It is the rate of change of angular position. Its unit is radians/second.
ω= dӨ/dt.

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