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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThe position vector of a particle in a rotating rigid body is given by \( \vec{r} = (3\hat{i} + 4\hat{j} - 2\hat{k})\text{ m} \) with respect to the origin on the axis of rotation. If the angular velocity of the rigid body is \( \vec{\omega} = (2\hat{i} - 3\hat{j} + \hat{k})\text{ rad/s} \), the linear velocity of the particle is:
Correct answer · Option 4
\( (2\hat{i} + 7\hat{j} + 17\hat{k})\text{ m/s} \)
Explanation
\( \vec{v} = \vec{\omega} \times \vec{r} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & -3 & 1 \\ 3 & 4 & -2 \end{vmatrix} = \hat{i}(6 - 4) - \hat{j}(-4 - 3) + \hat{k}(8 - (-9)) = 2\hat{i} + 7\hat{j} + 17\hat{k}\text{ m/s} \).
