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Consider an object A of a rigid body undergoing rotation about a fixed axis- , the particle A defining an arc ABA′ of a circle with its centre O on the axis of motion. Taking the origin at O, the position vector of A,
OA = OA′ = constant (radius of the circle)
∠A′OA = θ (t) (say)
The arc length, ABA′, S = rθ
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The tangential velocity, vA = 
The position of the angular velocity vector 
be taken along the axis of rotation:
is the unit vector along the axis of rotation.
Then,
, instantaneous velocity of A with respect to the axis of motion, can be written as ,
The acceleration of the point A related to the axis of rotation is
If is constant, then 
and 
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