Question 637: Centre of Mass and Rotational Motion

Question

The moment of the force, $$\overrightarrow F  = 4\widehat i + 5\widehat j - 6\widehat k$$ at
(2, 0, –3), about the point (2, –2, –2), is given by

Accepted Answer

Given, $$\overrightarrow F  = 4\widehat i + 5\widehat j - 6\widehat k$$
We know,
Moment of force, $$\overrightarrow 	au   = \left( {\overrightarrow r  - {{\overrightarrow r }_0}} ight) 	imes \overrightarrow F $$
Where $${\overrightarrow r _0} = 2\widehat i - 2\widehat j - 2\widehat k$$
and $$\overrightarrow r  = 2\widehat i + 0\widehat j - 3\widehat k$$
$${\overrightarrow r  - {{\overrightarrow r }_0}}$$ = $$\left( {2\widehat i + 0\widehat j - 3\widehat k} ight) - \left( {2\widehat i - 2\widehat j - 2\widehat k} ight)$$
= $${0\widehat i + 2\widehat j - \widehat k}$$
$$\overrightarrow 	au   = \left( {\overrightarrow r  - {{\overrightarrow r }_0}} ight) 	imes \overrightarrow F $$
= $$\left| {\matrix{
   {\widehat i} & {\widehat j} & {\widehat k}  \cr 
   0 & 2 & { - 1}  \cr 
   4 & 5 & { - 6}  \cr

} } ight|$$
= (-12 + 5)$${\widehat i}$$ - (+4)$${\widehat j}$$ + (-8)$${\widehat k}$$
= $$ - 7\widehat i - 4\widehat j - 8\widehat k$$

Answer

$$ - 8\widehat i - 4\widehat j - 7\widehat k$$

Answer

$$ - 4\widehat i - \widehat j - 8\widehat k$$

Answer

$$ - 7\widehat i - 8\widehat j - 4\widehat k$$

Answer

$$ - 7\widehat i - 4\widehat j - 8\widehat k$$

Centre of Mass and Rotational Motion

The moment of the force, $\overrightarrow F = 4\widehat i + 5\widehat j - 6\widehat k$ at (2, 0, –3), about the point (2, –2, –2), is given by

Choose the correct answer: