Simple question on acceleration and angular acceleration

[spacelike]

Homework Statement

I'm just reading a graduate level mechanics book for enjoyment/practice and I just need a push in the right direction with one of the problems.

It has a cylinder that is wrapped with a string around the circular part. The string is then pulled (so the force is tangential to the surface of the cylinder) and I have to find the angular acceleration, and the acceleration of the cylinder.

(see attached image, the circle represents the cylinder as you are looking down its axis and the red line is the string wrapped around the cylinder. The force is acting along the string to the right.)

Homework Equations

The Attempt at a Solution

I know how to do this if the axis of the cylinder were fixed, I would just find torque and then angular acceleration.

But the axis is not fixed,
So my question, and what I'm confused about, is how do I know how the force is divided between contribution to total acceleration and angular acceleration

At first I want to say that it all still goes into torque only since the force is always tangential to the surface, but if I think about pulling something like that in real life I would imagine that the whole object would move as well since it's not being held in place.

Can anyone give me a little advice?

 

[ehild]

A force exerted on a rigid body causes both acceleration of the centre of mass and rotation (about the centre of mass).
If that cylinder is in the empty space so only the tension in the string acts on it, the acceleration is a_CM=F/m and the angular acceleration is the torque with respect to the CM divided by the moment of inertia.

ehild

 

[spacelike]

Wow I didn't know it would be that simple.

I was thinking that $a_{CM}$ would be less than the total force over mass because some of it would go into causing angular acceleration.

Thanks for the explanation ehild.

 

[ehild]

I was thinking that $a_{CM}$ would be less than the total force over mass because some of it would go into causing angular acceleration.

It would be so if you pulled the cylinder on a horizontal surface, and there was friction between the ground and the cylinder. But the friction is an additional force, opposite with the tension, so the acceleration of the CM would be less than F/m: a=(F-Fr)/m.

ehild