A bug is on the rim of a 78 rev/min, 12 in. diameter record. The record moves from rest to its final angular speed in 2.91 s. Find the bug’s centripetal acceleration 1.5 s after the bug starts from rest. (1 in = 2.54 cm). Answer in units of m/s 2 .

Centripetal Acceleration = 2.701 m/s²

Explanation:

Given:

Starting from rest so initial angular velocity  ωi = 0 rad/s

Final angular velocity ωf= 78 rev/min =78 × 2π /60 rad/s = 8.168 rad/s

Radius of Rim =d/2 =12/6= 6 in = 6× 2.54 cm =15.24 cm = 0.1524 m

angular acceleration α = (ωf - ωi)/t = (8.168 rad/s - 0 rad/s)/2.91 s

α =2.807 rad/s²

now to find angular velocity at 1.5 s we have

ω = α × t =  2.807 rad/s² × 1.5 s = 4.210 rad/s

so centripetal acceleration ac = ω² r =  (4.210 rad/s)² × 0.1524 m

ac= 2.701 m/s²

A quantity that has magnitude and direction. It's usually represented by an arrow whose direction is the same direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude