# Rotary (Gears) question - angular acc/velocity involved

Rotary (Gears) question -- angular acc/velocity involved

## Homework Statement ## Homework Equations

w (angular velocity) = alpha (angular acceleration) t
w1 / w2 = r2 / r1
|a| = sqrt( (a(tangential))^2 + (a(normal))^2 )

## The Attempt at a Solution

Since A has a constant angular 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... wC = (150^2 * 14 * 0.8) / 250^2 = 4.032 rad/s

Now

wA = 0
alpha A = 14

and

wC = 4.032
alpha C = (r1 * alpha A) / r2 = 8.4

So

a(tangential) = alpha C * r2 = 2.1
a(normal) = (wC)^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?

It would be greatly appreciated, thank you

## Answers and Replies

I ended up getting the right answer.

alpha C = (r1 * alpha A) / r2 = 8.4
shouldve been
alpha C = (r1/r2)^2 * alpha A