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
$P =\vec{\tau}. \vec{\omega} = ( \vec{r} \times \vec{F} ) . \vec{\omega}$