# Classical Mechanics

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## Overview

Mechanics is the study of movement. Kinematics, mechanical forces, work, power, energy, and matter are all part of mechanics.

Kinematics is the study of (relative) motion - displacement, velocity, acceleration etc. The two relations at the heart of kinematics are: $\delta x'(t)=v(t)$ and $v'(t)=a(t)$ where $\delta x(t)$ is displacement at time $t$, $v$ is velocity, $a$ is acceleration, and $t$ is time. Uniform rectilinear motion, projectile motion, uniform circular motion, and simple harmonic motion are some of the types of problems studied in kinematics.

The rules of physics are almost fully summarized by the three famous laws of motion formulated by Isaac Newton:

• A body continues to be in its state of uniform rectilinear motion until it is disturbed by an external force. This property is known as inertia.
• The rate of change of momentum of a body with respect to time is directly proportional to the force acting on it.
• Every action has an equal and opposite reaction.

Mass is one of the two most basic intrinsic properties of a body. It is a measure of its inertia. Momentum is defined as the product of the mass and velocity of a body. Force is something that changes or tends to change the momentum of a body, or, informally, "a push or pull".

Mechanical work is defined by the relation $W =\int^{x_f}_{x_i} F\,dx$ where $W$ is work done, $F$ is force, $x$ is displacement, and subscripts $i$ and $f$ denote the initial and final states respectively. Similarly, mechanical power is defined as $P =\int^{v_f}_{v_i} F\,dv$ where $P$ is power delivered and $v$ is velocity. Energy is the other basic intrinsic property of a body. Mechanical energy is simply the capacity of a body to do mechanical work.

Among the various properties of matter are elasticity, surface tension, and viscosity. The most important one is gravity. Gravity is indeed considered one of the most mysterious things not only in physics but in science as a whole.