Acceleration of Center of Mass in Rotational Motion

I have a question regarding the acceleration of the center mass during rotational motion.

From my understanding, Fnet = m*a(center of mass).

Also, Torque = angular acceleration * moment of inertia.

Would this mean that the same force can do a different amount of work on an object depending on where it is applied?

For example, consider a rod floating in space. If it is pushed by force F at its center of mass, there will be no torque. However, if it is pushed near one of its ends, there will be the same acceleration of the center of mass as before, plus some torque.

• Also torque in 3D is $\vec{\tau} = I \vec{\alpha} + \vec{\omega} \times I \vec{\omega}$ not just $\tau=I \alpha$ as stated. – ja72 Nov 9 '14 at 18:16
• Related answer physics.stackexchange.com/a/80449/392 – ja72 Nov 9 '14 at 18:22