Kinematics of Rigid Bodies in 3D

[yoft]

Homework Statement

Problem 15.18:

I've defined the positive J (fixed) axis along the pole pointing upwards and the positive X (fixed) axis going to the right, with both centered at the point of contact between the hoop and the pole, which I will refer to as point O. The rotating axes (lower case) are defined along the fixed axes at this particular moment.

Homework Equations

ω=Ω(J) + v/R(k) = Ω(j) + v/R(k)
α=(Ωv)/R(i) <-- derived from the first expression of ω
V_A = V_O + ω x r_A/O + V_A/O = v(j) - 2ΩR(k)
a_A = a_O + α x r_A/O + ω x (ω x r_A/O) + a_A/O = (-2Ω²R-2v²/R)(i)

The Attempt at a Solution

My issue is that my v²/R term in my final acceleration is off by a factor of 2. I get -240 ft/s²(i) when I should be getting -216 ft/s²(i). Can anyone point me towards the step that I multiplied by 2 when I shouldn't have?

 

[yoft]

Actually I found the problem, I left off the 2ω x V_A/O term in the acceleration formula. That adds in another V²/R term that solves my factor of 2.