Question

The value of x in rad/s is

• A. 8
• B. -8
• C. 6
• D. can't be calculated

Answer 1

Answer: (B)

-8

Answer 2

For a particle undergoing uniform circular motion, the velocity vector $\vec{v}$ is always perpendicular to the angular velocity vector $\vec{\omega}$. Therefore, their dot product must be zero. Given: $\vec{v} = 3\hat{i} + 4\hat{j}$ m/s $\vec{\omega} = x\hat{i} + 6\hat{j}$ rad/sec

$\vec{v} \cdot \vec{\omega} = 0$ $(3\hat{i} + 4\hat{j}) \cdot (x\hat{i} + 6\hat{j}) = 0$ $3x + (4)(6) = 0$ $3x + 24 = 0$ $3x = -24$ $x = -8$ rad/s