 1
 0
 Homework Statement
 A giant yoyo has a mass of 3 kg and a moment of inertia of 7.68 kg⋅m^2. The central spool has a radius of 0.8 m. As it falls, the string unwinds from the central spool without slipping. If the yoyo is released from rest, how fast will it be moving when it has fallen a distance of 1.5 meters?
 Homework Equations

## \tau=I\alpha ##
## \tau = r F ##
## x = x_o + vt + 1/2at^2 ##
## (V_ƒ)^2 = (V_o)^2 + 2ax ##
What I attempted to do first was find alpha and turn that into translational acceleration.
Taking mass of yoyo * radius of spool * gravity, (3kg)(0.8m)(9.81m/s^2) yielded 23.544 N*m, and dividing by I = 7.68 kg * m^2 yielded 3.065625 rad/s^2. Finally, multiplying by r = 0.8m gave me 2.4525 m/s^2.
I assumed I could simply use the kinematics equations then, after translating into linear motion, to find velocity at the distance, but every attempt I've made has been wrong. I tried using (Vƒ)^2 = (Vo)^2 + 2ax to give me a velocity, setting vo to 0. But that was incorrect. I also tried some weird thing with [ tex ] x = x_o + v*t + 1/2*a*t^2 [ /tex ] , setting x = 1.5m, x_o = 0, to find t, and using that result again to find v*t. Nothing has worked so far, and I'm not really sure where my thought process is going wrong! Thank you for reading!
Taking mass of yoyo * radius of spool * gravity, (3kg)(0.8m)(9.81m/s^2) yielded 23.544 N*m, and dividing by I = 7.68 kg * m^2 yielded 3.065625 rad/s^2. Finally, multiplying by r = 0.8m gave me 2.4525 m/s^2.
I assumed I could simply use the kinematics equations then, after translating into linear motion, to find velocity at the distance, but every attempt I've made has been wrong. I tried using (Vƒ)^2 = (Vo)^2 + 2ax to give me a velocity, setting vo to 0. But that was incorrect. I also tried some weird thing with [ tex ] x = x_o + v*t + 1/2*a*t^2 [ /tex ] , setting x = 1.5m, x_o = 0, to find t, and using that result again to find v*t. Nothing has worked so far, and I'm not really sure where my thought process is going wrong! Thank you for reading!