An insect trapped in a circular groove of radius $12 ext{ cm}$ moves steadily and completes $7$ rev

Question

An insect trapped in a circular groove of radius $12	ext{ cm}$ moves steadily and completes $7$ revolutions in $100	ext{ s}$. What is the magnitude of its centripetal acceleration?

Professor PC Thomas Classes · Answer

Angular speed $\omega = \frac{2\pi(7)}{100} \approx 0.44	ext{ rad/s}$. Centripetal acceleration $a_c = \omega^2 R = (0.44)^2(12) = 2.32	ext{ cm/s}^2 \approx 2.3	ext{ cm/s}^2$.