​ Prove the relation vector v = ω x r, where symbols have their usual meaning. ​

Question

Prove the relation \(\vec {\text v}=\vec\omega\times\vec r\), where symbols have their usual meaning.

OR

In U.C.M. (Uniform Circular Motion), prove the relation \(\vec {\text v}=\vec\omega\times\vec r\), where symbols have their usual meanings.

Answer 1

Analytical method:

i. Consider a particle performing circular motion in anticlockwise sense with centre O and radius r as shown in the figure.

ii. Let, \(\vec\omega\) = angular velocity of the particle

\(\vec {\text v}\) = linear velocity of the particle

\(\vec r\) = radius vector of the particle

iii. Linear displacement in vector form is given by,

iv. Taking limiting value in equation (1)