First slide

Torque

Question

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

Moderate

A

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

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

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

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

Solution

Moment of inertia
$\overset{⇀}{τ} = \vec{r} \times \vec{F}$
$\vec{r} = (2 - 2) \hat{i} + (0 - (- 2)) \hat{j} + ((- 3) - (- 2)) \hat{k}$
$= (2 \hat{j} - \hat{k})$
Hence torque of force F about O
$\vec{τ} = (2 \hat{j} - \hat{k}) \times (4 \hat{i} + 5 \hat{j} - 6 \hat{k}) = - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

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