Moment of Force – Rankers Physics

Moment of Force

The moment of the force, $\vec{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at $(2, 0, -3)$, about the point $(2, -2, -2)$ is given by (2018)

$-7\hat{i} - 8\hat{j} - 4\hat{k}$
$-4\hat{i} - \hat{j} - 8\hat{k}$
$-8\hat{i} - 4\hat{j} - 7\hat{k}$
$-7\hat{i} - 4\hat{j} - 8\hat{k}$

Solution:

The relative position vector is $\vec{r} = (2-2)\hat{i} + (0 - (-2))\hat{j} + (-3 - (-2))\hat{k} = 2\hat{j} - \hat{k}$. Torque is $\vec{\tau} = \vec{r} \times \vec{F} = (2\hat{j} - \hat{k}) \times (4\hat{i} + 5\hat{j} - 6\hat{k}) = -7\hat{i} - 4\hat{j} - 8\hat{k}$.

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