Angular Displacement

The angle subtended at the center of a circle by an arc alongwhich a body moves on the circumference in a given time is

called angular displacement. It is denoted by Δθ

In given Fig 5.1(b), point 'A' is the point of contact between wheel and ground. If we apply some force to the wheel it rotate in

counter clock wise direction, the position "A" of the wheel

changes to position "B" in time 't', making an angle "θ" with the

axis of the wheel. At a later time t + Δt, its position is C making an

angle θ+Δθ with the axis of the wheel. The angle θ defines the

angular displacement of A during time interval Δt.

For small value of Δθ, the angular displacement is a vector

quantity. This angle θ= /_ AOB is the angular displacement of

wheel after given a small push.

For anticlockwise rotation of OP, the angular displacement Δθ is

positive while for clock-wise rotation the angular displacement Δθ

is negative.

In order to determine the direction of angular

displacement, we use the 'right hand rule'

Right hand Rule

Grasp the axis of rotation in right hand with fingers curling

in the direction of rotation then the erect thumb indicates the

direction of angular displacement.

Angular displacement is measured in degrees, or revolutions or radians.

Radian: The Sl unit of angular displacement is radian. It is the angle subtended by an arc at the center

of the circle whose length is equal to the radius of circle.

Other units are degrees and revolution.

It is the angle subtended at centre of circle by 1/360th part of its circumference.

In one complete rotation, a rotating object subtends an angle of 360 degree. If the circular path

is divided into 360 equal parts then the angle subtended by each part at the center of the circle is

equal to one degree.

The angle subtended by a complete round trip of the body along the circumference of the circle

is called one revolution.

Define and Explain Angular Displacement