Question

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.

Answer 1

Answer:

t = 6.981s

Explanation:

Given:

$\alpha A = 90 rad/s^2$$

\omega_d = 600 rpm = 62.831 rad/s$

$(\omega_0) = 0 rpm$

RADIUS OF GEAR A ra = .015 m

rb = .05 m

rc = .025 m

rd = .075

$

\alpha B = \alpha A*(\frac{ra}{rb}) = 90 * \frac{.015}{.05}$

$\alpha B = 27 rad/s^2$

$\alpha C = \alpha B$

Therefore$\alpha C = 27 rad/s^2$

$\alpha D = \alpha C*(\frac{rc}{rb})$

              $= 27 * (\frac{.025}{.075})$

$\alpha D = 9 rad/s^2$

from angular motion analysis for a constant angular Velocity  we have

$\omega = (\omega_0) + \alpha D*t$

solving for t

$t = \frac{(\omega - \omega_0)}{\alpha D}$

$t = \frac{(62.832 - 0)}{9}$

t = 6.981s