Force acting on rotatble object

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SUMMARY

The discussion centers on the dynamics of a body subjected to a force "F" at point "P," with its center of gravity located at point "A." The body has a moment of inertia "I" and mass "M." The translational acceleration of the center of mass is determined by the equation F = M*a, while the angular acceleration is derived from the torque equation τ = I*α. This straightforward approach clarifies the relationship between linear and angular motion without requiring complex tricks.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of rotational dynamics (τ = Iα)
  • Familiarity with concepts of center of mass and moment of inertia
  • Basic principles of torque and angular acceleration
NEXT STEPS
  • Study the relationship between linear and angular motion in rigid body dynamics
  • Explore the derivation of the equations for translational and angular acceleration
  • Learn about the effects of external forces on the motion of rigid bodies
  • Investigate real-world applications of torque and moment of inertia in engineering
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of rotating bodies and the effects of applied forces.

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 ([itex]\tau = I \alpha[/itex]).
 
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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