An insect trapped in a circular groove of radius $12 \; cm$ moves along the groove steadily and completes $7$ revolutions in $100 \; s$.
$(a)$ What is the angular speed,and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector? What is its magnitude?

(N/A) This is an example of uniform circular motion. Here,radius $R = 12 \; cm$.
$(a)$ The angular speed $\omega$ is given by $\omega = 2 \pi \nu$,where $\nu = 7 / 100 \; Hz$.
$\omega = 2 \times 3.14 \times (7 / 100) = 0.44 \; rad/s$.
The linear speed $v$ is $v = \omega R = 0.44 \; rad/s \times 12 \; cm = 5.28 \; cm/s \approx 5.3 \; cm/s$.
$(b)$ The acceleration vector is not a constant vector because its direction changes continuously as the insect moves along the circle,even though it always points towards the center (centripetal acceleration).
The magnitude of the acceleration is $a = \omega^2 R = (0.44 \; s^{-1})^2 \times 12 \; cm = 0.1936 \times 12 \; cm/s^2 = 2.3232 \; cm/s^2 \approx 2.3 \; cm/s^2$.