Question

A ceiling fan is rotating at the rate of $3.5rps$ and its moment of inertia is $1.25kg{m}^2$. If the current is switched off, the fan comes to rest in $5.5s$. The torque acting on the fan due to friction is:

• A. $2.5Nm$
• B. $5Nm$
• C. $7.5Nm$
• D. $10Nm$

Answer 1

The correct option is B $5Nm$

We know that, the torque is given by

$\tau =I\alpha$

where $I$ is the moment of inertia and $\alpha$ is the angular acceleration.

$\alpha =\frac{d\omega }{dt}=\frac{3.5\times 2\pi }{5.5}=4rad-s^{-}2$

$\therefore \tau =I\alpha =1.25\times 4=5Nm$