Mastering Physics: Rotational Motion Around Two Cylinders

[lila.haj]

Homework Statement

The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of the cylinders? Assume that the cylinders turn on a frictionless axle. I know the answer is 3.5 rad/s².

Figure: http://session.masteringphysics.com/problemAsset/1176936/5/P7-59.jpg

Homework Equations

\alpha=τ/I
τ=rF
I=1/2*M*R²

The Attempt at a Solution

I tried calculating the net torque of the cylinders caused by the hanging masses. I then divided the net torque by the total inertia on the cylinders using the first equation listed above.

 

[SammyS]

Homework Statement

The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of the cylinders? Assume that the cylinders turn on a frictionless axle. I know the answer is 3.5 rad/s².

Figure: http://session.masteringphysics.com/problemAsset/1176936/5/P7-59.jpg

Homework Equations

\alpha=τ/I
τ=rF
I=1/2*M*R²

The Attempt at a Solution

I tried calculating the net torque of the cylinders caused by the hanging masses. I then divided the net torque by the total inertia on the cylinders using the first equation listed above.

What is the total moment of inertia of the combined cylinders?

 

[lila.haj]

What is the total moment of inertia of the combined cylinders?

They don't give it to you in the problem. Would I calculate the inertia on each disk and add those together to get the total inertia of the disk system?

 

[SammyS]

They don't give it to you in the problem. Would I calculate the inertia on each disk and add those together to get the total inertia of the disk system?

Yes. That's how I would do it.

 

[lila.haj]

Yes. That's how I would do it.

But once you find the inertia what would you do from there?

 

[SammyS]

But once you find the inertia what would you do from there?

Well, earlier you mentioned calculating the net torque.

How is the acceleration of each mass related to the angular acceleration of the compound cylinder?

 

[haruspex]

I tried calculating the net torque of the cylinders caused by the hanging masses. I then divided the net torque by the total inertia on the cylinders using the first equation listed above.

That overlooks the inertia of the two hanging masses. Safest is to assign a tension variable to each rope, an angular acceleration variable for the cylinders, and write out three free body equations.

 

[lila.haj]

I think it may be easier to post my work than trying to explain it. This is what I have done, and I am unsure where my error may be. Any help is greatly appreciated!

 

[SammyS]

I think it may be easier to post my work than trying to explain it. This is what I have done, and I am unsure where my error may be. Any help is greatly appreciated!

Easier, but very hard to read.

The acceleration is not the same for both blocks.