Question

What is the relation between angular velocity and angle of rotation

Answer 1

Angle of rotation

When objects rotate about some axis, rotates about its center—each point in the object follows a circular arc. The rotation angle is the amount of rotation and is analogous to linear distance. We define the rotation angle Δθ to be the ratio of the arc length to the radius of curvature:

Δθ=Δs/r

The arc length Δs is the distance traveled along a circular path. We know that for one complete revolution, the arc length is the circumference of a circle of radius r. The circumference of a circle is 2πr.  

Thus for one complete revolution the rotation angle is  Δθ = 2πr / r = 2π

Angular Velocity

angular velocity ω is defined as the rate of change of an angle.

ω = Δθ / Δt

where an angular rotation Δθ takes place in a time Δt. The greater the rotation angle in a given amount of time, the greater the angular velocity. The units for angular velocity are radians per second (rad/s).

Angular velocity ω is analogous to linear velocity v.  

v = Δs / Δt

From Δθ = Δs / r

Δs =  rΔθ.

Substituting this into the expression for v gives

v = r Δθ / Δt = r ω

or ω = v / r

It states that the linear velocity v is proportional to the distance from the center of rotation. We can also call this linear speed v of a point on the rim the tangential speed.  

HOPE THIS IS USEFUL.