Please draw diagram and show work for a-c. SmartArt Box Styles 9.2 Rotation with
ID: 1779997 • Letter: P
Question
Please draw diagram and show work for a-c. SmartArt Box Styles 9.2 Rotation with Constant Angular Acceleration . At t = 0s, a wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s2 applied to for the next 2 seconds, when the acceleration is discontinued. From then on, it turns 432 rad as it coasts to a stop keeping a constant acceleration. (a) through what total angle did the wheel turn between t = 0 s and the time it stopped. (b) At what time did the wheel stop? (c) What was the acceleration as it was slowing down?Explanation / Answer
(A) When accelerating,
theta1 = (24 x 2) + (30 x 2^2 / 2)
= 108 rad
after that , theta = 432 rad
total angle revolved = 540 rad
(b) at t = 2 sec, w = 24 + (2 x 30) = 84 rad/s
wf^2 - w0^2 = 2 alpha theta
0^2 - 84^2 = 2 (alpha)(432)
alpha = 8.17 rad/s^2
0 = 84 - 8.17 t
t = 10.3 sec
total time = 12.3 sec
(C) alpha = - 8.17 rad/s^2