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A plane, homogeneous disk may slide on a frictionless horizontal table. A cord is fastened to the disc and wrapped many times around the rim of the disc. The cord goes without friction through a small eyelet at the edge of the table and is connected to a mass

**m**. The mass of the disc is

**M**and its radius is

**R**. The system is started from rest and the cord is assumed to be taut throughout the motion. Ignore the mass of the cord.

http://ylle.eu/DSC00602.JPG (my sketch of the problem)

*Describe the velocity of the disc as a function of time.*

Here is what i have computed of equations so far.

The forces affecting the disc M must be M(d²x)/(dt²) = mg

The forces affecting the mass m must be m(d²x)/(dt²) = mg - S

The torque(N) exerted on M can be described as

N = mgR

The moment of inertia for a circular disk around its CM is

I = (1/2)MR²

The angular momentum is

L = Iw

Torque equals the change of angular momentum with respect to time

N = Iw'

N = (1/2)MR²w'

mgR = (1/2)MR²w'

And from this point i cant really seem to maky any more observations that can help me solve the problem.

I hope someone can clarify the problem for me

Thanks in advance

Mikkel