Classical Mechanics Overview

Classical Mechanics

Definition: Branch of physics that deals with the motion of objects and the forces acting upon them.
Key Concepts:
1. Newton's Laws of Motion:
  - First Law: An object at rest stays at rest, and an object in motion continues in a straight line at constant speed unless acted upon by a net external force.
  - Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
  - Third Law: For every action, there is an equal and opposite reaction.
2. Kinematics:
  - Study of motion without considering its causes.
  - Equations of motion for uniformly accelerated motion:
    - ( v = u + at )
    - ( s = ut + \frac{1}{2}at^2 )
    - ( v^2 = u^2 + 2as )
  - Variables:
    - ( u ): initial velocity
    - ( v ): final velocity
    - ( a ): acceleration
    - ( s ): displacement
    - ( t ): time
3. Dynamics:
  - Study of forces and their effects on motion.
  - Identifies different types of forces:
    - Gravitational force
    - Frictional force
    - Tension
    - Normal force
Energy:
- Kinetic Energy (KE): Energy of motion, given by ( KE = \frac{1}{2}mv^2 ).
- Potential Energy (PE): Stored energy based on position, e.g., gravitational potential energy ( PE = mgh ) (where ( h ) is height).
Work and Power:
- Work (W): Done when a force causes displacement, calculated as ( W = F \cdot d \cdot \cos(\theta) ).
- Power (P): Rate at which work is done; ( P = \frac{W}{t} ).
Momentum:
- The product of mass and velocity, given by ( p = mv ).
- Conservation of momentum: In a closed system, total momentum before an event equals total momentum after.
Rotational Motion:
- Describes objects spinning around an axis.
- Angular displacement, velocity, and acceleration relate to linear quantities.
- Key equations:
  - Torque (( \tau )): ( \tau = r \times F )
  - Moment of inertia (( I )): ( I = \sum mr^2 )
Gravitational Force:
- Governed by Newton's Law of Universal Gravitation: ( F = G \frac{m_1 m_2}{r^2} ) (where ( G ) is the gravitational constant, ( m_1 ) and ( m_2 ) are masses, ( r ) is distance).
Applications:
- Used in engineering, aerospace, mechanical systems, and more.
- Principles help in predicting motion and analyzing physical systems.

Classical Mechanics

Branch of physics studying object motion and forces acting on them.

Key Concepts

Newton's Laws of Motion
- First Law: Objects at rest stay at rest, objects in motion stay in straight lines at constant speeds unless acted upon by a net external force.
- Second Law: Acceleration is directly proportional to net force and inversely proportional to mass (F = ma).
- Third Law: Every action has an equal and opposite reaction.

Kinematics

Study of motion without considering its causes.
Equations of motion for uniformly accelerated motion:
- ( v = u + at )
- ( s = ut + \frac{1}{2}at^2 )
- ( v^2 = u^2 + 2as )
- Where:
  - ( u ): initial velocity
  - ( v ): final velocity
  - ( a ): acceleration
  - ( s ): displacement
  - ( t ): time

Dynamics

Study of forces and their effects on motion.
Different types of forces:
- Gravitational force
- Frictional force
- Tension
- Normal force

Energy

Kinetic Energy (KE): Energy of motion, given by ( KE = \frac{1}{2}mv^2 ).
Potential Energy (PE): Stored energy based on position, e.g., gravitational potential energy ( PE = mgh ) (where ( h ) is height)

Work and Power

Work (W): Done when a force causes displacement, calculated as ( W = F \cdot d \cdot \cos(\theta) ).
Power (P): Rate at which work is done; ( P = \frac{W}{t} ).

Momentum

Product of mass and velocity, given by ( p = mv ).
Conservation of momentum: In a closed system, total momentum before an event equals total momentum after.

Rotational Motion

Describes objects spinning around an axis.
Angular displacement, velocity, and acceleration relate to linear quantities.
Key equations:
- Torque (( \tau )): ( \tau = r \times F )
- Moment of inertia (( I )): ( I = \sum mr^2 )

Gravitational Force

Governed by Newton's Law of Universal Gravitation: ( F = G \frac{m_1 m_2}{r^2} ) (where ( G ) is the gravitational constant, ( m_1 ) and ( m_2 ) are masses, ( r ) is distance).