Question

A disc is rotating with angular velocity $\vec{\omega }$ about its axis. A force $\vec{F}$ acts at a point whose position vector with respect to the axis of rotation is $\vec{r}$ . The power associated with the torque due to the force is given by

• A. $\left(\vec{r}\times \vec{F}\right)\cdot \vec{\omega }$
• B. $\left(\vec{r}\times \vec{F}\right)\times \vec{\omega }$
• C. $\vec{r}\cdot \left(\vec{F}\times \vec{\omega }\right)$
• D. $\vec{r}\times \left(\vec{F}\cdot \vec{\omega }\right)$

Answer 1

Answer: (A)

Torque, $\vec{\tau }=\vec{r}\times \vec{F}$
$\therefore$ Power associated with the torque is
$P=\vec{\tau }.\vec{\omega }=(\vec{r}\times \vec{F}).\vec{\omega }$