Answer:
6.41m/s2
Explanation:
unit conversion:
78 rev/min = 78rev/min * 2π rad/rev * 1/60 min/sec = 8.168 rad/s
12 in = 12 in * 2.54cm/in = 30.48 cm = 0.3048 m
So the record accelerate from rest to 8.168 rad/s, its (assuming constant) angular acceleration would be
[tex]\alpha = \Delta \omega / t = (8.168 - 0) / 2.67 = 3.06 rad/s^2[/tex]
From here we can calculate the angular velocity of the bug at t2 = 1.5s
[tex]\omega_2= \alpha*t_2 = 3.06 * 1.5 = 4.59 rad/s[/tex]
Its centripetal acceleration would then be
[tex]a = \omega_2^2*R = 4.59^2*0.3048 = 6.41 m/s^2[/tex]
