#Newton's First Law: Inertia and Equilibrium

#Introduction

Newton's First Law, also known as the law of inertia, is a cornerstone of physics. It essentially says that objects like to keep doing what they're already doing. 💡 This means an object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless a net force acts on it. This concept is crucial for understanding translational equilibrium and how forces affect motion.

#Conditions for Constant Velocity

#Vector Sum of Forces

• Calculating the net force 🎯 is key: you need to add all forces acting on an object as vectors. This means considering both their magnitude and direction.
• Forces in the same direction are added, while forces in opposite directions are subtracted.
• If forces act at angles, you'll need to break them into components (x and y) before adding them up.

#Translational Equilibrium

• Translational equilibrium occurs when the vector sum of all forces acting on an object equals zero. This means there's no net force, and thus no acceleration.

• Mathematically, it's represented as: $$Sigma F_{i} = 0$$

• Where $\Sigma$ represents the sum of all forces ($F_{i}$) acting on the system, and $i$ denotes each individual force.

• An object in translational equilibrium can be either at rest (static equilibrium) or moving at a constant velocity (dynamic equilibrium).

• Example: A book on a table is in static equilibrium; gravity pulls down, and the table pushes up with an equal force.

#Newton's First Law (Law of Inertia)

• Also known as the law of inertia ⚖️, it states that an object will maintain its state of m...