Question

write vector relation between angular velocity tangential veloc
ity and position vector

Answer 1

Let a particle moves with constant speed v m/s in tangential direction of circular path of radius r. if angular velocity of particle is $\omega$
then relation between v, r and $\omega$
is given by $\boxed{\bf{v=\omega\times r}}$
hence, tangential velocity of particle is the cross product of angular velocity and position vector of it.

magnitude of tangential velocity is given by
$|v|=\omega rsin\theta$
where $\theta$ is angle between $\omega$ and r.