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## Homework Statement

Two uniform disks with the same mass are connected by a light inextensible string supported by a massless pulley, on a frictionless axis. The string is attached to a point on the circumference of disk A. The string is wound around disk B so that the disk will rotate like a yo-yo when dropped. Describe the outcome when both disks hit the floor.

## Homework Equations

-ma=T-mg

Tr=(1/2)mr^2(alpha)

## The Attempt at a Solution

Okay I know that the two tensions are equal because the pulley is massless. I wanted to prove it to myself with equations which is the right answer. I decided that the translation accelerations for each mass would be different because one has the string wound around it and the other is simply hanging by the string.

I wasn't sure though what to make the direction of both accelerations, I just assumed negative for the calculations below:

Disk A

-ma=T-mg

Disk B

Tr=1/2mr^2(A/r)

T=mA/2

-mA=T-mg

I substituted T=mA/2 into the second equation for disk B to get:

-mA=mA/2 - mg

mA=mg- mA/2

3A/2=g

A= 6.53

Then I solved for T and just put the mass as 1kg

T= 6.53/2=3.27

Then I used T to solve for a for disk A

-a= 3.27 - 9.8

a= 6.53

Does this seem right at all? They both accelerate the same in magnitude, but opposite in direction?

I think I remember being my teacher doing something like a + A = 0, but I may have just imagined it.

Confirmation or correction would be amazing! Thanks!