Question

The power rating of a ceiling fan rotating with a constant torque of 2 Nm with an angular speed of 2\(\pi\) rad/s will be ............

• A. \(\pi\) W
• B. 2\(\pi\) W
• C. 3\(\pi\) W
• D. 4\(\pi\) W

Hint:

Rotational power is the rotational analogue of linear power (\(P = F \times v\)). Just replace force (F) with torque (\(\tau\)) and linear velocity (v) with angular velocity (\(\omega\)).

Answer 1

The Correct Option is D

The power (P) in a rotational system is given by the product of torque (\(\tau\)) and angular speed (\(\omega\)). \[ P = \tau \times \omega \] Given:
Torque, \(\tau = 2\) Nm
Angular speed, \(\omega = 2\pi\) rad/s
Substituting the values: \[ P = 2 \, \text{Nm} \times 2\pi \, \text{rad/s} = 4\pi \, \text{W} \] The power rating of the ceiling fan is \(4\pi\) W.