Angular Velocity and Radius Vector Cross Product – Rankers Physics

Kinematics of Circular Motion: Practice Problem & Solution

For a body angular velocity $\vec{\omega} = \hat{i} - 2\hat{j} + 3\hat{k}$ and radius vector is $\vec{r} = \hat{i} + \hat{j} + \hat{k}$ then its velocity is: (1999)
$-5\hat{i} + 2\hat{j} + 3\hat{k}$
$-5\hat{i} + 2\hat{j} - 3\hat{k}$
$-5\hat{i} - 2\hat{j} + 3\hat{k}$
$-5\hat{i} - 2\hat{j} - 3\hat{k}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Kinematics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Velocity is given by $\vec{v} = \vec{\omega} \times \vec{r}$. Evaluating the cross-product determinant yields $-5\hat{i} + 2\hat{j} + 3\hat{k}$.

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