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## Homework Statement

A solid body consisting in two concentric disks of masses

**m1**,

**m2**and radius

**r1<r2**is linked through a ideal rope to a mass

**m**which falls down with a certain acceleration. The solid body moves of pure rolling.

Find the acceleration

**a**of the mass.

## Homework Equations

P-T=m*a

T-F=(m1+m2)*A

I=1/2*m1*r1^2+1/2*m2*r2^2

T*r1+F*r2=I*alpha

**S**Q=w*r1+Scm or

**S**q=w*r1

**a**=

**a**Q=alpha*r1+A or

**a**=

**a**Q=alpha*r1

A=alpha*r2

## The Attempt at a Solution

The mass

**m**is subject to its weight force P=m*g and the tension T of the rope so:

P-T=m*a

T-F=(m1+m2)*a

On the solid body the tension and the grip of the floor (F) act:

T-F=(m1+m2)*A

I chose the center of mass (cm) as the pole of momentum of forces:

T*r1+F*r2=I*alpha

I=1/2*m1*r1^2+1/2*m2*r2^2

now I tried to find a relation between a and alpha: the acceleration and the speed of the piont Q has to be equal to the speed and the acceleration of the mass because the rope can't extend. So

**S**Q=w*r1+Scm and a=

**a**Q=alpha*r1+A (indeed I don't know if

**S**Q=w*r1+Scm or simply

**S**Q=w*r1 in fact, in the solution of the problem I found that

**S**Q=w*(r1+r2) but it has chosen the point P as pole for the momentum on the forces which ita speed is istant by istant naught). Since the body rolls without slither, the acceleration A of the center of mass and alpha must satisfy the condition A=alpha*r2.

I solved the sistem of equations (I tried both the equations for the speed) but in any case my solution was wrong. I hope you can help me.

Thanks a lot