Physics: Vectors and Equilibrium Forces

Vector Components

• The horizontal component of a vector can be calculated using the formula: ( V_x = V \cdot \cos(\theta) ), where ( V ) is the vector's magnitude and ( \theta ) is the angle with respect to the horizontal axis.

Free-Body Diagrams

• In free-body diagrams, forces exerted by the object itself, such as internal forces, are generally not included. Only external forces acting on the object are represented.

Principle of Moments

• The principle of moments states that for a body in rotational equilibrium, the sum of clockwise moments about a pivot point must equal the sum of counterclockwise moments about the same point.

Couples in Physics

• A couple consists of two equal and opposite forces acting on an object, creating a rotational effect without causing any translation. The moment of a couple produces rotational motion.

Stable Equilibrium

• A body is said to be in stable equilibrium when, if displaced slightly, it returns to its original position. This occurs when the center of mass is at its lowest potential energy state.

Unit of Moment

• The unit for moment in physics is Newton-meter (Nm). This unit reflects the force (in Newtons) multiplied by the distance from the pivot point (in meters).