Question

prove the relation v =w * r where symbols have their usual meanings​

Answer 1

The formula for the length of arc will be  

S = r θ

Where, r is the radius of circle, S is arc length and θ  is the angular displacement.

Dividing on both sides by t  

S/t = r θ/t

S/t becomes V whereas θ/t  becomes ω. Thus:

V = rω

Which is the relationship between the linear velocity and angular velocity when radius of the circle remains constant.