Question

A ceiling fan is rotating with an angular velocity of $4rev/s$. It takes $40s$ to stop when it is switched off. The angular retardation during this interval is

• A. $\frac{3\pi }{5}rad/s^2$
• B. $-\frac{\pi }{5}rad/s^2$
• C. $\frac{\pi }{5}rad/s^2$
• D. $\frac{2\pi }{5}rad/s^2$

Answer 1

The correct option is C $\frac{\pi }{5}rad/s^2$

We know that ${\alpha }_{avg}=\frac{{\omega }_f-{\omega }_i}{t_f-t_i}$
Given ${\omega }_i=4\text{rev/s}=4\times 2\pi \text{rad/s}=8\pi \text{rad/s}$
and ${\omega }_f=0$
Retardation, $\therefore {\alpha }_{avg}=\left|\frac{0-8\pi }{40}\right|=\frac{\pi }{5}rad/s^2$