Answer:
t = 6.981s
Explanation:
Given:
[tex]\alpha A = 90 rad/s^2[/tex][tex]
\omega_d = 600 rpm = 62.831 rad/s[/tex]
[tex](\omega_0) = 0 rpm[/tex]
RADIUS OF GEAR A ra = .015 m
rb = .05 m
rc = .025 m
rd = .075
[tex]
\alpha B = \alpha A*(\frac{ra}{rb}) = 90 * \frac{.015}{.05}[/tex]
[tex]\alpha B = 27 rad/s^2[/tex]
[tex]\alpha C = \alpha B[/tex]
Therefore[tex] \alpha C = 27 rad/s^2[/tex]
[tex]\alpha D = \alpha C*(\frac{rc}{rb})[/tex]
[tex]= 27 * (\frac{.025}{.075})[/tex]
[tex]\alpha D = 9 rad/s^2[/tex]
from angular motion analysis for a constant angular Velocity we have
[tex]\omega = (\omega_0) + \alpha D*t[/tex]
solving for t
[tex]t = \frac{(\omega - \omega_0)}{\alpha D}[/tex]
[tex]t = \frac{(62.832 - 0)}{9}[/tex]
t = 6.981s