# Rolling yo-yo and weight

1. May 28, 2008

### lehel

1. The problem statement, all variables and given/known data
a 16lb yo-yo is resting on a horizontal table and is free to roll. The dimensions are r = 4in and R = 12in and the radius of gyration about the CM is 6in. A cord is wrapped around the inner radius, the passes over a perfect pulley, and is attached to a 8lb block.

Find acceleration of 8lb block and the tension in the cord

2. Relevant equations

F = ma
torque = I*alpha = F*moment-arm
Iaxis = Icm + mh^2

3. The attempt at a solution

there are two accelerations a1 (weight) and a2 (yo-yo).

(16/32slugs)*a2 = T

I at table contact point = 90slug*in^2

net torqe at table contact point = 90slug*in^2 * alpha = T(12in - 4in)

T = 11.25*alpha and 0.5slugs * a2 = T

for weight, (8/32slugs)a1 = 8lb - T

so far, I have 4 unknowns and 3 equations so I can't solve for anything. What equation am I missing? i dont know how to find a relationship between alpha and a2 (i thought a2 = 12in*alpha but that doesn't work out right).