Q.The power rating of a ceiling fan rotating with a constant torque of 2 Nm with an angular speed of 2π rad/s will be ______.

Torque $\vec{\tau}$ (the moment of a force) is rotational mechanics' analogue of force. For a rigid body of particles at perpendicular distances $r_i$ from a fixed axis, all rotating together with a common angular acceleration $\alpha$, each particle experiences a tangential force $f_i=m_ir_i\alpha$, contributing a torque $\tau_i=m_ir_i^2\alpha$. Summing over every particle of the body (all torque contributions pointing along the same fixed axis, so they simply add) gives $\tau=I\alpha$ where $I=\sum m_ir_i^2$ is the moment of inertia -- the direct rotational analogue of Newton's second law $F=ma$, with I replacing mass m. …