Question

If gear a rotates with a constant angular acceleration of aa = 90 rad>s2, starting from rest, determine the time required for gear d to attain an angular velocity of 600 rpm. Also, find the number of revolutions of gear d to attain this angular velocity. Gears a, b, c, and d have radii of 15 mm, 50 mm, 25 mm, and 75 mm, respectively.

Answer 1

`Given: (let a = alpha)</p><p>aA = 90 rad/s^2</p><p>(wd) = 600 rpm = 62.831 rad/s</p><p>(w0) = 0 rpm</p><p>ra = .015 m</p><p>rb = .05 m</p><p>rc = .025 m</p><p>rd = .075</p><p>aB = aA*(ra/rb) = 90 * (.015/.05)</p><p>aB = 27 rad/s^2</p><p>aC = aB, Therefore aC = 27 rad/s^2</p><p>aD = aC*(rc/rb) = 27 * (.025/.075)</p><p>aD = 9 rad/s^2`
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