Solve Rotational Problem: Find Disc Velocity as Function of Time

[MikkelR]

I'm kinda stuck in this mechanical problem, ill try to describe the situation.

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 can't 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

 

[OlderDan]

You need to rethink the force acting on the disk. Look at what you did for the hanging mass and think about the connection between the two objects.