Rotary (Gears) question

dimanche 29 septembre 2013

1. The problem statement, all variables and given/known data

2. Relevant equations

w = alpha t

w1 / w2 = r2 / r1

|a| = sqrt( (a(tangential))^2 + (a(normal))^2 )

3. The attempt at a solution

Since it has a constant acceleration, w = alpha t

For gears A, B: wA/wB = r2/r1

For gears B, small B: wB = w(small B)

For gears small B, C: wC = r1/r2 * ((r1*wA) / r2)

Thus wC = ((r1)^2 * wA) / (r2)^2

And thus wC = ((r1)^2 * alpha * t) / (r2)^2

Subbing in values... (150^2 * 14 * 0.8) / 250^2 = 4.032

Now

wA = 0

alpha A = 14

wD = 4.032

alpha D = (r1 * alpha A) / r2 = 8.4

a(tangential) = alpha D * r2 = 2.1

a(normal) = (wD)^2 * r2 = 4.064

|a| = sqrt( 2.1^2 + 4.064^2) = 4.57

However this is not correct...

Could someone point out where I may have gone wrong?

Greatly appreciated, thanks