Force acting on rotatble object

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A force "F" acting on a body at point "P" while its center of gravity is at "A" results in both translational and angular acceleration. The translational acceleration of the center of gravity can be calculated using F = ma, where "m" is the mass of the body. Additionally, the force creates a torque that leads to angular acceleration, which can be determined using τ = Iα, with "I" being the moment of inertia. The discussion clarifies that the relationship between the force and the resulting accelerations is straightforward, without any special tricks involved. Understanding these principles is essential for analyzing the motion of rotating objects.
LonelyStar
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Hi everybody,
I've the following problem:
I have a force "F" pulling a body at point "P" while the center of gravity of the body is at "A". The Body has a Moment of Inertia of "I" and a mass of "M".

The question is: What is the acceleration of the centre of gravity and what is the angular acceleration of the body.

If the centre of gravity would be fixed, I would know what to do, but it is not.
If "A-P" and "F" would be in linear relation to each other, the solution would be F=M*a, would it not?

But what happens in general?

Any help/Ideas?
Thanks!
Nathan
 
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translation plus rotation

That force will produce a translational acceleration of the center of mass (F = ma) as well as exert a torque about the center of mass producing an angular acceleration about the center of mass (\tau = I \alpha).
 
OK, did not know that it is that simple. I thought there would be some special trick to it.
Thanks!
Nathan
 

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