Why are the components of position vectors al | vedclass

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Question

(A) The torque $\vec{	au}$ is defined as the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$,given by $\vec{	au} = \ve

Vedclass · Accepted Answer

Because they are parallel to the axis of rotation.

Vedclass · Answer

(A) The torque $\vec{	au}$ is defined as the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$,given by $\vec{	au} = \vec{r} 	imes \vec{F}$.When calculating the torque about a specific axis,we consider the component of the position vector $\vec{r}$ that is perpendicular to the axis of rotation.Any component of the position vector $\vec{r}$ that lies along the axis of rotation is parallel to the axis.Since the cross product of any vector with a vector parallel to the axis of rotation results in a component that is perpendicular to the axis,the parallel components of $\vec{r}$ do not contribute to the torque component along that axis.Therefore,only the perpendicular components of the position vector are relevant for determining the torque about a given axis.

Why are the components of position vectors along the axis of rotation not needed for determining the torque in a rigid body?

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