Question

An insect moves in a circular path of radius $\frac{20}{\pi }\text{cm}$ steadily, and completes 25 revolutions in $100\text{s}$. What is the average angular speed and the average linear speed of the motion ?

• A. $\frac{\pi }{2}\text{rad/s},1\text{m/s}$
• B. $\frac{\pi }{2}\text{rad/s},0.1\text{m/s}$
• C. $\pi \text{rad/s},0.1\text{m/s}$
• D. $\pi \text{rad/s},1\text{m/s}$

Answer 1

The correct option is B $\frac{\pi }{2}\text{rad/s},0.1\text{m/s}$

Average angular speed $\overline{\omega }=\frac{\Delta \theta }{\Delta t}=\frac{25\times 2\pi }{100}=\frac{\pi }{2}\text{rad/s}$
Average linear speed
$\overline{v}=\overline{\omega }R=\frac{\pi }{2}\times \frac{20}{\pi }=10\text{cm/s}$
$=0.1\text{m/s}$