If gear A rotates with a constant angular acceleration of αA= 90 rad/s2 , starting from rest, determine the time required for gear D to attain an angular velocity of 600 rpm. Gears A, B, C, and D have radii of 15 mm, 50 mm, 25 mm, and 75 mm, respectively.

Respuesta :

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

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