Question

There is a disk rotating with a constant angular speed of 18 rad/sec. At some instant the disk begins to experience a constant friction resulting in an angular acceleration of 1.4 rad/sec²

Find:

1) the time (in sec) it takes the disk to come to a complete stop due to friction

2) total number of complete revolutions the disk undergoes before coming to a complete stop due to friction;

3) the time (in sec) it takes the disk to complete 8 full revolutions (be careful here!).

Answer 1

1)

w = w_o + $\alpha$ t

0 = 18 + ( - 1.4) t

t = 18 / 1.4

t = 12.86 seconds

______________

2)

w² - w_o² = 2$\alpha$$\theta$

0² - 18² = 2 * -1.4 * $\theta$

$\theta$ = 115.7 radians

so,

Number of turns = $\theta$ / 2* pi

N = 18.416 ( or 18 full revolutions)

________________

3)

8 full revolutions means 8 * 2 * pi = 50.265 rad

so,

$\theta$ = w_ot - 1/2$\alpha$t²

50.265 = 18t - 0.7t²

0.7t² - 18t + 50.265 = 0

t = 18 +/ - 13.54 / 2 * 0.7

t = 3.186 seconds