Classical Mechanics Basics

First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.
Second Law (F=ma): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Third Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Displacement: Change in position of an object.
Velocity: Rate of change of displacement; can be average or instantaneous.
Acceleration: Rate of change of velocity; can be uniform or non-uniform.
Equations of Motion (for constant acceleration):
- ( v = u + at )
- ( s = ut + \frac{1}{2}at^2 )
- ( v^2 = u^2 + 2as )

Forces: Push or pull on an object. Types include:
- Gravitational
- Frictional
- Tension
- Normal
Free Body Diagrams: Visual representation of forces acting on an object.

Work (W): Done when a force causes displacement. ( W = F \cdot d \cdot \cos(\theta) )
Kinetic Energy (KE): Energy of motion. ( KE = \frac{1}{2}mv^2 )
Potential Energy (PE): Energy stored due to position. ( PE = mgh ) (gravitational)
Conservation of Energy: Total energy in an isolated system remains constant.

Linear Momentum (p): Product of an object's mass and velocity. ( p = mv )
Conservation of Momentum: In a closed system, total momentum before an interaction equals total momentum after.

Torque (τ): Measure of the force that causes an object to rotate. ( τ = r \cdot F \cdot \sin(\theta) )
Angular Velocity (ω): Rate of change of angular position.
Moment of Inertia (I): Resistance to change in rotation; depends on mass distribution.

Simple Harmonic Motion (SHM): Type of periodic motion where restoring force is proportional to displacement.
Wave Properties: Frequency, wavelength, amplitude, and speed.

Newton's Law of Universal Gravitation: Every point mass attracts every other point mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Classical mechanics examines object motion and forces involved.
Incorporates essential principles like Newton's Laws, conservation laws, and kinematics.

First Law (Inertia): Objects remain at rest or in uniform motion unless acted upon by a net external force.
Second Law: Acceleration (a) is proportional to net force (F) and inversely proportional to mass (m), expressed as ( F = ma ).
Third Law: Every action has an equal and opposite reaction, highlighting the mutual nature of forces.

Displacement represents the change in position of an object.
Velocity measures the rate of displacement, categorized as average or instantaneous.
Acceleration indicates the rate of velocity change, which can either be uniform (constant) or non-uniform (varying).
Key equations for constant acceleration:
- ( v = u + at ) (final velocity equation)
- ( s = ut + \frac{1}{2}at^2 ) (displacement equation)
- ( v^2 = u^2 + 2as ) (relationship involving final velocity)

Forces can be classified as gravitational, frictional, tension, or normal.
Free Body Diagrams visualize all forces acting on an object, aiding analysis of motion.

Work (W) is performed when a force causes displacement, calculated by ( W = F \cdot d \cdot \cos(\theta) ).
Kinetic Energy (KE) represents energy due to motion, given by ( KE = \frac{1}{2}mv^2 ).
Potential Energy (PE) is stored energy based on position, with gravitational potential energy expressed as ( PE = mgh ).
The principle of conservation of energy states that total energy in an isolated system remains constant.

Linear Momentum (p) is defined as the product of an object's mass and velocity, ( p = mv ).
The conservation of momentum principle states that in an isolated system, total momentum before and after an interaction remains unchanged.

Torque (τ) measures the effectiveness of a force in causing rotation, calculated by ( τ = r \cdot F \cdot \sin(\theta) ).
Angular Velocity (ω) indicates how fast an object rotates.
Moment of Inertia (I) quantifies an object's resistance to changes in its rotational motion, depending on mass distribution.

Simple Harmonic Motion (SHM) is characterized by periodic motion where restoring force corresponds directly to displacement.
Wave properties include frequency, wavelength, amplitude, and speed, essential for analyzing wave dynamics.

Newton's Law of Universal Gravitation states that every mass attracts every other mass, with the force proportional to the product of their masses and inversely proportional to the square of their separation distance.

Engineering fields utilize classical mechanics for structure and machinery design.
In astrophysics, mechanics aids in understanding planetary movements and broader cosmology.
Everyday applications encompass vehicle dynamics, sports motion analysis, and more.