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,
![2343_Relation between linear and angular variables.png](https://www.expertsmind.com/../CMSImages/2343_Relation between linear and angular variables.png)
OA = OA′ = constant (radius of the circle)
∠A′OA = θ (t) (say)
The arc length, ABA′, S = rθ
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![2419_Relation between linear and angular variables1.png](https://www.expertsmind.com/../CMSImages/2419_Relation between linear and angular variables1.png)
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The tangential velocity, vA = ![1494_Relation between linear and angular variables2.png](https://www.expertsmind.com/../CMSImages/1494_Relation between linear and angular variables2.png)
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
![751_Relation between linear and angular variables7.png](https://www.expertsmind.com/../CMSImages/751_Relation between linear and angular variables7.png)
If
is constant, then
and ![224_Relation between linear and angular variables10.png](https://www.expertsmind.com/CMSImages/224_Relation%20between%20linear%20and%20angular%20variables10.png)
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