can you answer question number 4,5,6, 7 please Chp. 10: Rotational Kinematics A

Question

can you answer question number 4,5,6, 7 please Chp. 10: Rotational Kinematics A bug is riding on a music CD at a point 5 cm from the center. The CD starts rotating at t = 0, and accelerates uniformly, reaching its final rotational speed of 500 rpm in 5 seconds. (1) At t = 1 s, what is the bug's angular acceleration alpha, in (rad)/s^2? (2) At t = 1 s, what is the bug's tangential acceleration aT, in m/s^2? (3) At t = 1 s, what is the bug's rotational speed w, in (rad)/s? (4) At t = 1 s, what is the bug's linear (tangential) speed v, in m/s? (5) At t = 1 s, what is the bug's centripetal acceleration ac, in m/s^2? (6) At t = 3s, what is the bug's linear (tangential) speed v, in m/s? (7) At t = 3s, what is the bug's tangential acceleration aT, in m/s^2? (8) At t = 3s, what is the bug's centripetal acceleration ac, in m/s^2?

Explanation / Answer

(1) n = 500 rpm = 500/60 = 8.33 rev/sec

? = 2?n = 2 x 3.14 x 8.33= 52.31 rad/sec

?(final) = ?(initial) + ?t

=>? =52.31/1= 52.31 rad/s^2

(2)a = r?= 5 x 10^-2 x 52.31=2.61 m/sec^2

(3) ? = 2?n = 2 x 3.14 x 8.33= 52.31 rad/sec

(4) By v = r?= 5 * 10^-2 * 52.31=2.61 m/sec

(5)ac= v^2 / r= 136.2 m/s^2

(6)v = r?= 5 * 10^-2 * 52.31=2.61 m/sec

(7)?(final) = ?(initial) + ?t

=>? =52.31/3 = 17.43 rad/sec^2

(8)ac= v^2 / r= 136.2 m/s^2

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