Learning Outcomes

Upon completing this lesson, you will be able to:

• Define Mechanics and distinguish between its two main branches: Statics and Dynamics.
• Identify and explain the four fundamental concepts of mechanics: Space, Time, Mass, and Force.
• State Newton's Three Laws of Motion and explain their significance as the foundation of classical mechanics.
• Understand the importance of a consistent system of units, primarily the SI system.
• Differentiate between scalar and vector quantities and provide examples of each.

Topics Covered

• What is Mechanics?
• Newton's Three Laws of Motion
• Units and Dimensions
• Scalars and Vectors

I. What is Mechanics?

Mechanics is the branch of physical science that deals with the state of rest or motion of bodies that are subjected to the action of forces. It is the foundational science for virtually all fields of engineering, as it provides the principles for analysis and design of both stationary structures and moving machinery.

The study of mechanics is typically divided into two areas:

1. Statics: This is the study of bodies in equilibrium. A body is in equilibrium if it is at rest or moving with a constant velocity. Statics is primarily concerned with ensuring that structures and systems are stable and can withstand the forces applied to them.
2. Dynamics: This is the study of bodies in motion. It explores the relationship between the forces acting on a body and the resulting motion, specifically the acceleration it experiences.

II. Newton's Three Laws of Motion

Classical mechanics is built upon a set of axioms that describe the relationship between forces and the motion of objects. These are Sir Isaac Newton's Three Laws of Motion, which are considered the starting point for our analysis.

• Newton's First Law (The Law of Inertia): An object will remain at rest, or continue to move with a constant velocity, unless it is acted upon by a net external force.
  • Inertia is the property of an object to resist changes in its state of motion. Mass is a measure of inertia.
• Newton's Second Law (The Law of Acceleration): The acceleration $(a)$ of an object is directly proportional to the net force $(F_{net})$ acting on it and inversely proportional to its mass $(m)$.
  • This is the most famous equation in mechanics: $\Sigma \vec{F} = m\vec{a}$
• Newton's Third Law (The Law of Action-Reaction): For every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction.

III. Units and Dimensions

In mechanics, we deal with four fundamental quantities: length, mass, time, and force. The relationship between them is defined by Newton's Second Law $(F=ma)$. This means we only need to define units for three of them, and the fourth can be derived.

A. The SI System (International System of Units)

The SI system is the modern form of the metric system and is the standard used in science and engineering worldwide.

• Length: meter $(m)$
• Mass: kilogram $(kg)$