IIT (NTSE/Olympiad)  

Circular Motion & Rotational Dynamics

3. Relation Between Linear Velocity And Angular Velocity

3. Relation between linear velocity and angular velocity
We have
[∴ dθ = , angle = and v = = linear velocity]
⇒ v = rω
In vector form,
Note :
(i) When a particle moves along a curved path, its linear velocity at a point is along the tangent drawn at that point
(ii) When a particle moves along curved path, its velocity has two components. One along the radius, which increases or decreases the radius and another one perpendicular to the radius, which makes the particle to revolve about the point of observation.

IIT (Class X)