What is the downward acceleration?

[deanwudean]

A yoyo consists of aunfirom disk with a string wound around the rim. the upper end of the string is held fixed. the yoyo unwinds as it drops. what is the downward acceleration?

I got the idea that Inertia*acceleration=force on the rim.

 

[Doc Al]

Consider the forces acting on the disk and the torques they produce. Apply Newton's 2nd law to both translational and rotational motion.

 

[deanwudean]

I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?

 

[Doc Al]

I got it ,F=(M+lc/(R^2))ac

Mg=ac(M+(1/2MR^2)/(r^2)
ac=g/(1+R^2/2r^2)

If the yo-yo is just a uniform disk with the string wound around the rim, this answer can be simplified.

just one more question, I can't figure out the accerlation of a slipping cylinder in a ramp.

how to apply slipping force, I mean the kinetic frictional force>?

Just add the friction force to the mix. It equals $\mu N$.