Classical Mechanics Concepts

Definition: Classical mechanics is the branch of physics that deals with the motion of objects and the forces acting upon them, primarily at a scale that is much larger than atomic.

Newton's Laws of Motion:
- First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion 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 (Action-Reaction): For every action, there is an equal and opposite reaction.
Kinematics:
- Describes the motion of objects without considering the forces involved.
- Key equations include:
  - ( v = u + at ) (final velocity)
  - ( s = ut + \frac{1}{2}at^2 ) (displacement)
  - ( v^2 = u^2 + 2as )
Dynamics:
- The study of forces and their effect on motion.
- Involves concepts like:
  - Weight: ( W = mg ) (mass times gravitational acceleration).
  - Friction: A force opposing motion, characterized by coefficients of static and kinetic friction.

Conservation of Energy: Total energy in an isolated system remains constant (kinetic + potential energy).
Conservation of Momentum: Total momentum in an isolated system remains constant unless acted upon by external forces.

Linear Motion:
- Motion along a straight path, described by position, velocity, and acceleration.
Rotational Motion:
- Motion about a central axis, characterized by angular displacement, angular velocity, and angular acceleration.
- Key equations involve torque (( \tau = rF )) and moment of inertia (( I = \sum mr^2 )).
Projectile Motion:
- Motion of objects thrown into the air, exhibiting a parabolic trajectory under the influence of gravity.
- Key components to analyze: horizontal and vertical motion independently.

Work: Defined as the product of force and displacement in the direction of the force (W = Fd cos θ).
Kinetic Energy: Energy of an object due to its motion (( KE = \frac{1}{2}mv^2 )).
Potential Energy: Energy stored in an object due to its position (gravitational potential energy ( PE = mgh )).

Free Body Diagrams: Visual representations that show all the forces acting on an object.
Types of Forces:
- Gravitational
- Normal
- Frictional
- Tension
- Applied forces

Classical mechanics is used in various fields including engineering, astrophysics, and everyday life scenarios like vehicle motion and sports dynamics.

Classical mechanics studies the motion and forces on objects at macroscopic scales, involving everyday phenomena.

Newton's Laws of Motion:
- First Law: Resting objects remain still; moving objects remain in motion unless influenced by an external force.
- Second Law: Acceleration (( a )) depends on net force (( F )) and mass (( m )) according to ( F = ma ).
- Third Law: Every action has an equal and opposite reaction, establishing a reciprocal relationship between forces.
Kinematics:
- Focuses on describing motion without considering forces, characterized by:
  - ( v = u + at ): Relates final velocity to initial velocity, acceleration, and time.
  - ( s = ut + \frac{1}{2}at^2 ): Calculates displacement based on initial velocity, time, and acceleration.
  - ( v^2 = u^2 + 2as ): Connects velocities and displacement.
Dynamics:
- Examines the influence of forces on motion, introducing concepts such as:
  - Weight: Given by ( W = mg ), where ( g ) is gravitational acceleration.
  - Friction: A resisting force with distinct coefficients for static and kinetic friction.

Conservation of Energy: Energy within isolated systems remains unchanged, combining kinetic and potential forms.
Conservation of Momentum: Momentum remains consistent in isolated systems unless external forcing changes occur.

Linear Motion: Straight-line movement defined by position, velocity, and acceleration.
Rotational Motion: Movement around an axis, incorporating angular quantities such as displacement, velocity, and acceleration, along with relevant equations:
- ( \tau = rF ): Describes torque as the product of radius and force.
- ( I = \sum mr^2 ): Defines moment of inertia, summing mass at respective distances from the axis.
Projectile Motion: Objects travel in parabolic paths influenced by gravity, analyzed through separate horizontal and vertical components.

Work: Calculated as ( W = Fd \cos θ ), where ( F ) is the force, ( d ) is the displacement, and ( θ ) is the angle.
Kinetic Energy: Expressed as ( KE = \frac{1}{2} mv^2 ); dependent on an object's mass and velocity.
Potential Energy: Represents stored energy, particularly gravitational potential energy as ( PE = mgh ).

Free Body Diagrams: Diagrams illustrating all acting forces on an object for analysis.
Types of Forces:
- Gravitational
- Normal
- Frictional
- Tension
- Applied forces

Classical mechanics applies to engineering, astrophysics, and practical scenarios like vehicle motion and sports dynamics, illustrating its relevance in real-world contexts.