Torque Problem, acceration of mass. Help!

mmmboh

I'm sorry, I feel stupid but I don't really understand. I know that C_x is the x-component of the center of mass, my issue is why A_x-C_x=k-rθ...Because lets say the center of mass of the cylinder doesn't move, then k-rθ is how much closer the mass is to the cylinder, in other words then A_x-C_x=k-rθ..but lets say the cylinder rotates that same amount, but this time C_x also moves, then the equation would predict the same result, but obviously it's not the same because now the cylinder is closer to the mass...

Sorry, but what is my constraint equation?

I have never had this much trouble understanding a problem

Thanks for your help by the way.

tiny-tim

no, because the mass has also moved, in this case the same amount as the cylinder (if the rotation is the same)
A_x - C_x = k - rθ …

a constraint equation is a geometrical equation rather than a force equation … like a body being constrained to move along a particular surface, or in this case the free length of string being constrained to be connected to the position and rotation of the bodies

mmmboh

Ok but, I used that constraint equation already to find α to plug it into my torque equation...

The three equations are T+t=ma
(T-t)r=Iα=0.5mr²α
A_x - C_x = k - rθ, so differentiating this twice I can solve for α.

So I get T+t=ma_cylinder, and T-t=0.5m(a_cylinder-a_mass), and then I'm stuck.

tiny-tim

ah, but you also have t = -ma_mass