Question

If \[ \overline{V}=x^{2}y\,\overline{i}-yz^{2}\,\overline{j}+xyz\,\overline{k} \] is the linear velocity of a particle in circular motion at the point \((1,1,1)\), then its angular velocity is

• A. \(-\frac{1}{2}(\overline{i}+\overline{j}+\overline{k})\)
• B. \(0\)
• C. \(\frac{1}{2}(3\overline{i}-\overline{j}-\overline{k})\)
• D. \(\frac{1}{2}(\overline{i}+\overline{j}+\overline{k})\)

Hint:

Whenever a velocity field is given and angular velocity is required, remember the standard relation \[ \vec\omega=\frac12(\nabla\times\vec V). \] First compute the curl and then divide by \(2\).

Answer 1

The Correct Option is D