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## Homework Statement

One pulley, on one side we have a block with mass m.

On the other side we have a cylinder with mass m.

Cylinder (radius R) has unlimited string (massless, negligible thickness, no slippage)

So you can imagine two blocks falling as more string unravels from the cylinder.

I am told that these two objects have the same acceleration downwards. Why?

## Homework Equations

F=ma

ma=mg-T

torque? T*R=I*[itex]\alpha[/itex]

## The Attempt at a Solution

The problem made it sound like this was a quick, obvious argument.

I proceeded to a longer argument, finding that the accelerations of both masses were (2/3)g downward:

starting with the cylinder-

TR=I*[itex]\alpha[/itex]

T*R

^{2}= (1/2)M*R

^{2}* a

Finding T= (1/2)ma, then plugging T back into the standard F=ma equations.

Then I find the acceleration of the block to be (2/3)g as well.

Is this even right? If it is, was there a way to show that the objects' accelerations were the same without finding the actual accelerations?

The reason I don't think this is right is because I did the problem using conservation of energy using the assumption that the objects fell down at the same acceleration.

With conservation of energy I got acceleration=(1/2)g (conserving KE, PE, angular KE)