Question

Write vector relation between angular velocity $\left(\overrightarrow{\omega }\right)$, tangential velocity $\left(\overrightarrow{V}\right)$ and position vector $\left(\overrightarrow{r}\right)$.

Answer 1

Any quantity or an unit that has direction are called as vector units$.$

Here$,$

The angular velocity is directly proportional to the product of tangential velocity and position vector$.$

That is $,$ the angular velocity is equal to the tangential velocity if and only if they are equal in magnitude and in direction$.$

The relationship$,$

$Angularvelocity=\mathrm{Tan}gentialvelocity\times positionvector$

$w=v\times r$

The relationship holds true if and only if they are equal in magnitude and in direction$.$