Solving General Plane Motion Homework - Problem 19

[_Bd_]

Homework Statement

The teacher provided the solutions already.

http://www.swccd.edu/~lzinola/engr251/eightedition/ch15/ch15001.pdf

Page 2 Problem 19) the two wheels and a belt

Homework Equations

v = (omega) X r
a = (alpha) X r + (omega) X { (omega X r) }

The Attempt at a Solution

I understand the formulas and all but I don't understand where that (8/12) comes from. . .
in the formula it stands for r. . .but the radius of the wheel is 8,
the fomrula should be
v = w x r
so 12 = w x 8
and therefore w = 3/2
and also for alpha, why is it just alpha x r and not alpha x r + omega x (omega x r) ??
Thank you!

 

[tiny-tim]

Hi _Bd_!

(have an alpha: α and an omega: ω )

… the radius of the wheel is 8 …

erm … inches!

why is it just alpha x r and not alpha x r + omega x (omega x r) ??

That's the total acceleration formula …

here, a is only the tangential acceleration, and that double-cross term is the centripetal acceleration