Question

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

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

Answer 1

Answer: (A)

$\left( \overrightarrow{r} \times \overrightarrow{F} \right).\overrightarrow{\omega}$

Answer 2

Torque, $\overset{\rightarrow}{\tau} = \overset{\rightarrow}{r} \times \overset{\rightarrow}{F}$

$\therefore$Power associated with the torque is

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