# Force acting on rotatble object

• LonelyStar
In summary, the conversation discusses the problem of finding the acceleration of the center of gravity and the angular acceleration of a body being pulled by a force at a specific point. The solution involves using the equations F=ma and \tau = I \alpha, with the center of mass being the point of reference. The conversation concludes with the realization that the solution is simpler than expected.
LonelyStar
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

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

## 1. What is the definition of "force acting on a rotatable object"?

Force acting on a rotatable object refers to the external force that causes a change in the rotational motion of an object. This force can be applied at any point on the object and can cause it to rotate around an axis.

## 2. What are the common examples of forces acting on rotatable objects?

Some common examples of forces acting on rotatable objects include torque, friction, and magnetic force. Torque is the force that causes an object to rotate around an axis, while friction can resist this rotational motion. Magnetic force can also cause an object to rotate if it is acting on a magnetic material.

## 3. How is the direction of force acting on a rotatable object determined?

The direction of force acting on a rotatable object is determined by the direction of the applied force and the axis of rotation. The direction of the force is perpendicular to the radius of rotation, also known as the lever arm, and points in the direction of the rotation according to the right-hand rule.

## 4. What is the relationship between force and rotational motion of an object?

The relationship between force and rotational motion of an object is described by Newton's Second Law of Motion, which states that the net torque applied to an object is equal to the product of its moment of inertia and its angular acceleration. This means that a greater force can result in a faster rotational motion of an object.

## 5. How can the force acting on a rotatable object be calculated?

The force acting on a rotatable object can be calculated using the formula, F = I * α, where F is the net force applied, I is the moment of inertia of the object, and α is the angular acceleration. This formula can be applied to determine the force needed to achieve a certain rotational motion or to calculate the force acting on an object given its moment of inertia and angular acceleration.

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