# Yo-Yo problem

## Homework Statement

Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g

a. Determine the rotational inertia of a yo-yo about it's center.
b. Dervie using force and torque the expression for the linear acceleration of a yo-yo
c. Calculate the a of the yo-yo for the given values

I = (1/2)mr^2
Iα = τ

## The Attempt at a Solution

Part a. pretty simple, I think I did it right. Using the moment of inertia equation for a disk, just add 2xthe I of the disks, and the I of the axle, didn't have a problem for that, got 156gcm^2.

Part b. I wasn't completely sure if I was doing right. I started with mg-T = ma and went from there. τ=Fr, so the force in this case is the tension, so

τ=(mg-ma)r, and since τ= Ia, and also a = (a/r) I got eventually

a = mgr^2/(I-mr^2). Did I do this properly?

Part c. was plugging in the numbers. I was a little confused about r, r would be the radius of just the axel right? Using that, I got 20.4 cm/s^2.

I'm a little iffy on the whole thing, so hopefully I can get some help.

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kuruman
Homework Helper
Gold Member

## Homework Statement

Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g

a. Determine the rotational inertia of a yo-yo about it's center.
b. Dervie using force and torque the expression for the linear acceleration of a yo-yo
c. Calculate the a of the yo-yo for the given values

I = (1/2)mr^2
Iα = τ

## The Attempt at a Solution

Part a. pretty simple, I think I did it right. Using the moment of inertia equation for a disk, just add 2xthe I of the disks, and the I of the axle, didn't have a problem for that, got 156gcm^2.
The method is correct. Redo the numbers and if you get the same answer, you are OK here.

Part b. I wasn't completely sure if I was doing right. I started with mg-T = ma and went from there. τ=Fr, so the force in this case is the tension, so

τ=(mg-ma)r, and since τ= Ia, and also a = (a/r) I got eventually

a = mgr^2/(I-mr^2). Did I do this properly?
*** On edit ***
Not quite. Recheck the algebra.

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