# Question #a1106

Nov 28, 2015

Power in rotational motion = Torque . angular velocity ( $w$ )
Power = Scalar

#### Explanation:

Key point : Try to develop the study of rotational motion parallel to the study of translational motion .

In Translatory motion
If we apply a force ,say F, on an object , and the force causes a net displacement of the object , then we say work is done .
In that case we have , $W = F . s$.

Now , $P = \frac{W}{T}$ , here work done is that of translational motion.

In rotational motion
When a torque / moment of force ( analogue of force in rotational motion) causes a body to rotate by an angular displacement $\theta$ , then we have $W = T . \theta$

Similar to translational , $P = \frac{W}{T}$ ,here work done is that of rotational motion .

Now ,
P=dW/dt=Τ(dθ/dt)=Τω ( $d \theta$ is used here as a the angular displacement $\theta$ is very small)

In vector notation
P=Τ.ω ( since, $\frac{\theta}{t} = \omega$ )