Forces and Equilibrium

Basic Principles

Force is a vector quantity, possessing both a magnitude and direction.
The unit of force is the Newton (N) in the SI system.
Forces may be represented by vectors, drawn as arrows indicating the magnitude and direction of the force.
The resultant of multiple forces acting in various directions can be calculated by vector addition.

A body is in static equilibrium if it is at rest or moving at a constant velocity.
A body in equilibrium is subject to zero net force and zero net moment.
Equilibrium of forces involves both the balance of forces in all directions and the balance of moments about any point.
To solve equilibrium problems, balance forces in the horizontal and vertical directions, and then balance moments.

Moment of a force or torque is the turning effect of a force about a point or axis. It depends on the force’s magnitude, the perpendicular distance from the pivot point to the force’s line of action, and the sine of the angle between the force vector and the distance.
Principle of moments: The sum of clockwise moments about any point equals the sum of anti-clockwise moments about the same point, for a body in equilibrium.
A couple is a pair of forces with equal magnitudes, opposite directions and different lines of action, creating a rotational effect.

A body is in translational equilibrium if the vector sum of all forces acting on it is zero, meaning there is no resulting force to cause translational motion.
For a body in equilibrium, the x-component and y-component of the resultant force must both be zero.

Work done by a force is the product of the force and the displacement in the direction of the force.
Principle of conservation of energy: Energy can neither be created nor destroyed, it can only be transformed from one form to another.
Mechanical energy includes both kinetic energy (due to motion) and potential energy (due to position).

Newton’s First Law (Law of Inertia): An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by a resultant force.
Newton’s Second Law: The rate of change of momentum of a body is directly proportional to the resultant force causing it and takes place in the direction in which the force acts.
Newton’s Third Law: To every action, there is an equal and opposite reaction.