- #1

adjurovich

- 119

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Thread moved from the technical forums to the schoolwork forums

We are asked to find the tension in the rope. First from the first, we can assume that tensions in both ropes are equal, so we can treat them as a single rope since they are wound symmetrically. That “rope” will act tangentially to both cylinders so it exerts torque, the torque equations are:

##Iα_1=RT##

##Iα_2=RT##

We can clearly see that angular accelerations are equal.

By adding these two equations and rearranging them, we get:

##α=\dfrac{4T}{mR}##

It all makes sense. However, I am confused about the accelerations part:

The upper cylinder has only tangential acceleration, and the no-slipping condition says:

##a_{tan} = a_{rope}##

So: ##Rα=a_{rope}##

For the lower body, its net acceleration will be:

##a - R \alpha = a_{rope}##

Now, if I got it right, we can treat this acceleration ##a## (translational) as the component of net tangential acceleration since every point has equal acceleration ##a## but so does the point tangential to the cylinder?

And thus by combining these two we get:

##a = 2R\alpha##

I understand the rest so I will stop here. Please correct me if I’m wrong.

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