A bug is riding on a music CD at a point 5 cm from the center, The CD Starts rot

Question

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 uniformaly, reaching its final rotational speed of 500 rpm in 5 seconds. (1) At t=1s. what is the bug?s angular acceleration in(rad)/s^2? (2) At t=1s, what is the bugs tangential acceleration alpha r, in m/s2? (3) At t=1s, what is the bug?s rotational speed w, in (rad)/s? (4) At t=1s, what is the bug?s linear (tangential) speed V, in m/s? (5) At t=1s, what Is the bug?s centripetal acceleration ac, in m/s2? (6) At t=3s, what is the bug?s linear (tangential) speed V, in m/s? (7) At=3s, what Is the bug?s tangential acceleration era, in m/s2? (8) At t=3s, what is the bug?s centripetal acceleration ac, in m/s2?

Explanation / Answer

wf = 500 rpm = 500*2*3.14/60 = 52.33 rad/s

1) alfa = (wf-wo)/2 = (52.33-0)/5 = 10.47 rad/s^2

2) a_tan = r*alfa = 0.05*10.47 = 0.5235 m/s^2

3) w = wo + alfa*t = 10.47*1 = 10.47 rad/s

4) v = r*w = 0.05*10.47 = 0.5235 m/s

5) ac = v^2/r = 0.5235*0.5235/.05 = 5.48 m/s^2

6) v = at*t = 0.5235*3 = 1.5705 m/s

7) at = r*alfa = = 0.05*10.47 = 0.5235 m/s^2

8) ac = v^2/r = 1.5705*1.5705/.05 = 49.33 m/s^2

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