Question

Question #a1106

Answer 1

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 = 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 = 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, `theta / t = omega` )