# Static of a rigid body

We call a rigid body or extended body, any object that cannot be described by a point.

To know the balance in these cases it is necessary to establish two concepts:

## Center of mass

An extended body can be considered a system of particles, each with its mass.

The total resultant of particle masses is the total mass of the body. Let CM be the point at which we can consider all body mass concentrated, this point will be called the body's Center of Mass.

For symmetrical bodies that have uniform mass distribution, the center of mass is the geometric center of the system itself. As with a homogeneous sphere, or a perfect cube.

For the other cases, the calculation of the center of mass is made by the weighted arithmetic average of the distances of each point of the system.

To calculate the center of mass we need to know its coordinates on each axis of the Cartesian plane above, taking into account the mass of each particle:

So the Center of Mass of the above particle system is located at (1.09, 0.875), ie:

As a generic form of the center of mass formula we have:

## Moment of a force

Imagine a person trying to open a door, will they need to push harder if pushed against the opposite end of the hinge, where the door handle is, or in the middle of the door?

Clearly we realize that it is easier to open or close the door if we apply force to its end, where the doorknob is. This happens because there is a quantity called Force Moment , which can also be called Torque.

This quantity is proportional to the Force and the application distance from the turning point, ie:

The momentum unit of force in the international system is the Newton-meter (N.m)

Since this is a vector product, we can say that the Moment of Force module is:

Being:

M = Force Moment Module.

F = Force Module.

d = distance between the application of force to the turning point; lever arm.

sen θ = smallest angle formed between the two vectors.

How if the application of force is perpendicular to the d the moment will be maximum;

How when the application of force is parallel to the d, the moment is null.

And the direction and direction of this vector is given by the Right Hand Rule.

The Moment of Strength of a body is:

• Positive when turning counterclockwise;
• Negative when turning clockwise;

Example:

What is the moment of force for a 10N force applied perpendicular to a door 1.2m from the hinges?