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**HELP!!!A rolling without slipping problem**

## Homework Statement

A solid cylinder of radius R and mass M has a string wrapped around it and is placed on its side on a horizontal surface. The free end of the string is pulled horizontally with a force F as shown in the figure. As the string unwraps, the cylinder rolls along the surface without slipping.

a) show that the acceleration of the center of mass is given by a_cm=4F/3M

b) what is the magnitude and direction of the frictional force acting on the cylinder?

c) what is the acceleration of the free end of the string?

diagram:

http://tinypic.com/view.php?pic=2qsw4kj&s=4

## The Attempt at a Solution

V_cc=0 and it is the velocity at reference frame of center to center

a) accelertaion of CM:

A_tot=sqrt((a

_{tan})

^{2}+(a

_{c})

^{2})

=sqrt((R*alpha)

^{2})

^{2}+(R*(V

_{cc})

^{2})

because v

_{cc}=0 therefore A_tot=R*alpha

4F/3M=4(M*alpha)/3M=4/3*alpha and R=4/3 in this case

b) the frictional force opposite to the applied force, and it is equal to the applied force, which is equal to M*alpha

c) the acceleration of the free end of the string would be same as the acceleration of the cylinder, which is R*alpha

I am not sure whether I did the problem correctly or not, can anyone help me with it? thank you very much.