Quick ? about gravitational torque

[bocobuff]

Homework Statement

A string wrapped around a cylinder(M=2.15kg, R=0.131m) on a frictionless thin bearing pulls downward with F=6.769N. Also, the string is on the right side of the cylinder. What is angular acceleration?

I know moment of Inertia=1/2*M*R² for cylinder = 0.01845kg*m².
I know angular accel=Torque_net/I
So the torque of the string pulling down will be negative because the cylinder is rotating cw and the string is vertical so sin90=1 which means Torque_string=-6.769N*0.131m=-0.8867N*m

Now for the Torque_grav=-MgX_cm where cm=center of mass, will the Xcm be equal to the radius and positive because it is to the right of the axle/bearing? Or will there not even be a Torque_grav because the axle/bearing is already on the center of mass? Or will Xcm=1 so Torque_grav=-Mg?

 

[Redbelly98]

... Or will there not even be a Torque_grav because the axle/bearing is already on the center of mass? ...

That's right. F_grav can be treated as acting at the center of mass ... which is located at exactly 0 m from the center of mass.