Applied Physics -> Mechanics -> Classical Mechanics

Description:

Classical Mechanics, a fundamental sub-discipline within Applied Physics and Mechanics, is concerned with the principles and laws governing the motion of macroscopic objects. It predominantly focuses on the behavior of solid matter under the influence of various forces and encompasses the kinematics and dynamics of physical systems.

At the core of Classical Mechanics are several pivotal concepts and laws discovered by Sir Isaac Newton, thus it is often referred to as Newtonian Mechanics. These include:

1. Newton’s Laws of Motion:
   • First Law (Inertia): An object at rest stays at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by an external force. \[ \sum \vec{F} = 0 \implies \vec{v} = \text{constant} \]
   • Second Law (Force and Acceleration): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. \[ \vec{F} = m \cdot \vec{a} \]
   • Third Law (Action and Reaction): For every action, there is an equal and opposite reaction. \[ \vec{F}{12} = -\vec{F}{21} \]
2. Kinematics: This branch deals with the description of motion without considering its causes. It includes:
   • Displacement, Velocity, and Acceleration: \[ \text{Displacement: } \vec{x}(t) \] \[ \text{Velocity: } \vec{v}(t) = \frac{d\vec{x}(t)}{dt} \] \[ \text{Acceleration: } \vec{a}(t) = \frac{d\vec{v}(t)}{dt} = \frac{d^{2\vec{x}(t)}{dt}2} \]
3. Dynamics: This field concerns the forces and torques that result in the movement of bodies. Key concepts include:
   • Work-Energy Theorem: \[ W = \Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 \]
   • Conservation of Energy: \[ E = K + U = \text{constant} \] where \( K \) is the kinetic energy and \( U \) is the potential energy.
   • Conservation of Momentum: \[ \vec{p} = m\vec{v} \] \[ \sum \vec{F}{ext} = \frac{d\vec{p}}{dt} \implies \sum \vec{F}{ext} = 0 \implies \vec{p} = \text{constant} \]
4. Rotational Motion: Explores the motion of bodies rotating about an axis. Includes:
   • Angular Displacement, Velocity, and Acceleration: \[ \theta(t), \quad \omega(t) = \frac{d\theta(t)}{dt}, \quad \alpha(t) = \frac{d\omega(t)}{dt} \]
   • Moment of Inertia: \[ I = \sum m_i r_i^2 \]
   • Torque and Rotational Analog to Newton’s Second Law: \[ \tau = I \cdot \alpha \]

Classical Mechanics is not only vital for theoretical understanding but also has numerous practical applications. Engineers, physicists, and other scientists use these principles to design and analyze buildings, vehicles, machines, and even predict planetary motion. Despite its limitations in explaining phenomena at atomic scales and at speeds close to the speed of light (where Quantum Mechanics and Relativity take over), Classical Mechanics remains a cornerstone of modern applied physics, providing a comprehensive framework for understanding and manipulating the macroscopic world.