Statics:
Statics is the branch of mechanics that is concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves at constant velocity.
According to Newton's first law, the net force and net torque also known as moment of force on every part of the system is zero. From this constraint, such quantities as stress or pressure can be derived. The net forces equaling zero is known as the first condition for equilibrium, and the net torque equals to zero is known as the second condition for equilibrium.
Vectors
A scalar is a quantity, such as mass or temperature, which only has a magnitude. A vector has a magnitude and a direction and obeys the parallelogram law. Vectors are added using the parallelogram law or the triangle law. Vectors contain components in orthogonal bases. Unit vectors i, j, and k along the x, y, and z axes, respectively.
Force
Force is the action of one body on another. A force is either a push or a pull. A force tends to move a body in the direction of its motion. The motion of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Thus force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action.
Moment of Force
In addition to the tendency to move a body in the direction of its application, a force can also tend to rotate a body about an axis. The axis may be any line which neither intersects nor is parallel to the line of action of the force. This rotational tendency is known as the moment of the force. Moment is also referred to as torque.
Moment about a point
The magnitude of the moment of a force at a point O, is equal to the perpendicular distance from O to the line of action of F, multiplied by the magnitude of the force: W= Fd. In vector format, the moment can be defined as the cross product between the radius vector, r (the vector from point O to the line of action), and the force vector.
Varignon's theorem
Varignon's theorem states that the moment of a force about any point is equal to the sum of the moments of the components of the force about the same point.
Moment of Inertia
In classical mechanics, moment of inertia, also called mass moment, rotational inertia, polar moment of inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. The symbols I and J are usually used to refer to the moment of inertia or polar moment of inertia.
SOLIDS:
Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium
FLUIDS:
Hydrostatics, also known as fluid statics, is the study of fluids at rest (i.e. in static equilibrium). The characteristic of any fluid at rest is that the force exerted on any particle of the fluid is the same at all points at the same depth within the fluid. If the net force is greater than zero the fluid will move in the direction of the resulting force
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