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

t = 6.981s

Step-by-step explanation:

Given:

`\alpha A = 90 rad/s^2`
`</p><p>\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

`</p><p>\alpha B = \alpha A*((ra)/(rb)) = 90 * (.015)/(.05)`

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

`\alpha C = \alpha B`

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

`\alpha D = \alpha C*((rc)/(rb))`

`= 27 * ((.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 = ((\omega - \omega_0))/(\alpha D)`

`t = ((62.832 - 0))/(9)`

t = 6.981s