Kinetic energy of rotated cylinders

[steffan]

Homework Statement

You have a figure that is combined with three figures. Two solid cylinders and one rectangle in the middle. Like this: O[]O

The two cylinders is rotating and are not sliding, so the whole figure moves to the right. The rectangle is connected with the two cylinders. Both cylinders and the rectangle has each mass M, so it will be three masses: M1=M2=M3. Also the two cylinders has the same radius: r1=r2

Proof that the kinetic energy equals to 2Mv² (k=2Mv²)

Homework Equations

K=1/2Mv²=1/2M(r²w²)=1/2Iw²
I=1/2Mr² (for solid cylinders)

The Attempt at a Solution

2*1/2Iw²=2*1/2*1/2Mr²*w²=
2*1/2*1/2Mv²(energy of 2 cylinders)+1/2Mv²(energy of rectangel)=1Mv²

I don't understand why it should be 2...

 

[tiny-tim]

hi steffan!

2*1/2*1/2Mv²(energy of 2 cylinders)+1/2Mv²(energy of rectangel)=1Mv²

you've only included the rotational KE of the cylinders, you must add the linear KE

 

[steffan]

Oh, so it has both linear and rotational ke? Thanks a lot, I didn't knew that :)