Consider a particle revolving around a point O in a circle of radius r.

**Angular
displacement**

Consider
a particle revolving around a point O in a circle of radius r (Figure 2.45).
Let the position of the particle at time t = 0 be A
and after time t, its position is B.

Then,

*The angle described by the particle
about the axis of rotation (or center O) in a given time is called angular
displacement.*

i.e.,
angular displacement = ∠*AOB* =*θ*

The unit of angular displacement is radian.

The
angular displacement (θ) in radian is related to arc length S (AB) and
radius r as

*The rate of change of angular
displacement is called angular velocity.*

If
θ is the angular displacement in time t, then the angular velocity ω is

The
unit of angular velocity is radian per second (rad s^{−1}). The
direction of angular velocity is along the axis of rotation following the right
hand rule. This is shown in Figure 2.46.

*The rate of change of angular
velocity is called angular acceleration.*

The
angular acceleration is also a vector quantity which need not be in the same
direction as angular velocity.

Consider
an object moving along a circle of radius r. In a time ∆*t*, the object travels an arc distance ∆*s* as shown in Figure 2.47. The corresponding angle subtended
is Δθ

which
gives the relation between linear speed and angular speed.

Equation
(2.38) is true only for circular motion. In general the relation between linear
and angular velocity is given by

For
circular motion equation (2.39) reduces to equation (2.38) since and are perpendicular to each other.

Differentiating
the equation (2.38) with respect to time, we get (since r is constant)

The
tangential acceleration *a _{t}*
experienced by an object is circular motion as shown in Figure 2.48.

Note
that the tangential acceleration is in the direction of linear velocity.

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11th Physics : UNIT 2 : Kinematics : Angular displacement in Projectile Motion |

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