The relationship between linear velocity and angular velocity

In linear motion , when a body moves with uniform velocity , in time t , its linear displacement will be ;

S = r∅     S = vt

r∅ =  vt

r.∅ / t = v

As

v = rw

where ∅ = 90° is the angle between between radius vector r  and angular velocity w (omega )

In case ∅ ≠ 90° , we can write v = r w sin∅

It gives us v = w× r