If torque is calculated relative to a referen | vedclass

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(B) The torque $\vec{	au}$ about a point $P$ is defined as $\vec{	au} = \vec{r} 	imes \vec{F}$.If the reference point is displaced by a vector $\ve

Vedclass · Accepted Answer

No,it becomes invalid.

Vedclass · Answer

(B) The torque $\vec{	au}$ about a point $P$ is defined as $\vec{	au} = \vec{r} 	imes \vec{F}$.If the reference point is displaced by a vector $\vec{d}$,the new position vector becomes $\vec{r}' = \vec{r} - \vec{d}$.The new torque is $\vec{	au}' = (\vec{r} - \vec{d}) 	imes \vec{F} = (\vec{r} 	imes \vec{F}) - (\vec{d} 	imes \vec{F})$.For the condition of rotational equilibrium (i.e.,$\vec{	au} = 0$) to remain valid regardless of the choice of reference point,the term $\vec{d} 	imes \vec{F}$ must be zero.This occurs if the net force $\vec{F}$ is zero or if the displacement $\vec{d}$ is parallel to the net force $\vec{F}$.Therefore,in general,the torque changes when the reference point is shifted,unless the net force acting on the system is zero.

If torque is calculated relative to a reference point and this point is displaced,does the condition for rotation remain valid?

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