Question

An insect trapped in circular groove of radius 12 cm moves along the groove steadily and completes revolutions in 100 s. (a) What is the angular speed of motion? (b) Is the acceleration vector constant ? What is its magnitude?

Answer 1

Given : $r=12cm=0.12m$

Time to complete one revolution $t=100s$

Average speed $V_{avg}=\frac{2\pi r}{T}=\frac{2\pi \times 0.12}{100}=0.0075m/s=0.75cm/s$

Angular speed $w=\frac{v}{r}=\frac{0.0075}{0.12}=0.0625rad/s$

Centripetal acceleration changes its direction at every instant.

Magnitude of acceleration $a=\frac{v^2}{r}=4.7\times {10}^{-4}m/s^2=0.047cm/s^2$