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.
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:
I substituted T=mA/2 into the second equation for disk B to get:
-mA=mA/2 - mg
Then I solved for T and just put the mass as 1kg
Then I used T to solve for a for disk A
-a= 3.27 - 9.8
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!