- #1

ajb13t

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- Homework Statement
- A giant yo-yo 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 yo-yo is released from rest, how fast will it be moving when it has fallen a distance of 1.5 meters?

- Relevant 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!