I=5.805 kgm^2San Francisco YoYo Acceleration and Tension Calculations

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SUMMARY

The discussion focuses on the calculations related to the acceleration and tension of a large yo-yo, weighing 129 kg, consisting of two uniform disks with a radius of 30 cm and an axle radius of 3.2 cm. The acceleration during its fall and rise is determined using the equation a = -g/(1 + I/mr²), where I is the moment of inertia calculated as I = (mr²)/2 for a disk. The tension in the cord is derived from the net force equation, F(total) = ma = F(gravity) - F(tension), leading to F(tension) = mg - ma. The user successfully resolved the calculations for the moment of inertia and confirmed the correctness of their approach.

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Homework Statement


A large yo-yo is released from a crane over San Francisco Bay. The 129 kg yo-yo consists of two uniform disks of radius 30 cm connected by an axle of radius 3.2 cm.
(a) What is the magnitude of the acceleration of the yo-yo during its fall?
(b) What is the magnitude of the acceleration of the yo-yo during its rise?
(c) What is the tension in the cord on which it rolls?
Hint: Use the equation for rolling down a ramp.


Homework Equations


a= -g/(1+I/mr^2) is the equation it is referring to
For a disk, I=(mr^2)/2

The Attempt at a Solution


I'm stuck at finding I. I would apply the disk equation to each of the three disks in the yoyo. But it doesn't divide the three disks into their individual masses, so I don't know how to find I.
Parts A and B should be the same, correct?
And to find tension, F(total)=ma=F(gravity)-F(tension)=mg-F(tension), so F(tension)=mg-ma correct?


Update:
Resolved myself...I don't really understand why this was correct but it was.
I=((129 kg)(.3 m)^2)/2
 
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