Respuesta :
Answer:
[tex]\theta = 20\ rev[/tex]
Explanation:
Case 1
Given,
initial angular speed = 0 rev/s
final angular speed = 2 rev/s
time, t = 7 s
angular acceleration of the washer
[tex]\alpha = \dfrac{\omega_f-\omega_i}{t}[/tex]
[tex]\alpha = \dfrac{2-0}{7}[/tex]
[tex]\alpha = 0.286\ rev/s^2[/tex]
using equation of rotational motion
[tex]\omega_f^2 = \omega_i^2 + 2 \alpha \theta_1[/tex]
[tex]2^2 = 0^2 + 2\times 0.286 \times \theta_1[/tex]
[tex]\theta_1 = 7 rev[/tex]
Case 2
Given,
initial angular speed = 2 rev/s
final angular speed = 0 rev/s
time, t = 12 s
angular acceleration of the washer
[tex]\alpha = \dfrac{\omega_f-\omega_i}{t}[/tex]
[tex]\alpha = \dfrac{0-2}{13}[/tex]
[tex]\alpha = -0.154\ rev/s^2[/tex]
using equation of rotational motion
[tex]\omega_f^2 = \omega_i^2 + 2 \alpha \theta_2[/tex]
[tex]0^2 = 2^2 + 2\times (-0.154) \times \theta_2[/tex]
[tex]\theta_2 = 13 rev[/tex]
total revolution in this case
[tex]\theta = \theta_1 + \theta_2[/tex]
[tex]\theta =7 +13[/tex]
[tex]\theta = 20\ rev[/tex]
total revolution of the washer is equal to 20 rev.
