Unit 2965: Classical Mechanics

1. Introduction to Classical Mechanics

• Definition and scope of classical mechanics
• Historical context and significance in physics
• Overview of key concepts:
  • Newton's laws of motion
  • Conservation of energy
  • Conservation of momentum

2. Kinematics

2.1 Motion in One Dimension

• Displacement, velocity, acceleration
• Graphical analysis of motion
• Equations of motion for constant acceleration

2.2 Motion in Two and Three Dimensions

• Vector representation of position, velocity, acceleration
• Projectile motion
• Relative velocity

3. Dynamics and Newton's Laws

3.1 Newton's First Law: Law of Inertia

• Concept of inertia
• Reference frames

3.2 Newton's Second Law: F = ma

• Force and acceleration relationship
• Applications in various force scenarios

3.3 Newton's Third Law: Action-Reaction

• Interaction pairs
• Examples in real-world systems

4. Work and Energy

4.1 Work Done by a Force

• Definition and calculation
• Work done by variable forces

4.2 Kinetic Energy

• Definition and derivation
• Work-Energy theorem

4.3 Potential Energy

• Conservative and non-conservative forces
• Gravitational and elastic potential energy

5. Conservation of Energy

• Principle of conservation of mechanical energy
• Energy transformations in systems with conservative forces
• Applications and problem solving

6. Linear Momentum and Collisions

6.1 Momentum

• Definition and properties
• Impulse and change in momentum

6.2 Conservation of Momentum

• Isolated systems
• Elastic and inelastic collisions
• Center of mass motion

7. Rotational Motion

7.1 Rotational Kinematics

• Angular displacement, velocity, acceleration
• Relation between linear and angular quantities

7.2 Rotational Dynamics

• Torque and its calculation
• Moment of inertia and radius of gyration
• Rotational analogues of Newton's laws

7.3 Angular Momentum

• Definition and conservation
• Applications in rotational systems

8. Gravitation

8.1 Universal Law of Gravitation

• Newton’s law and gravitational constant
• Gravitational force between two masses

8.2 Gravitational Field

• Definition and field strength
• Field lines and potential

8.3 Gravitational Potential Energy

• Work done in gravitational fields
• Escape velocity and orbital motion

9. Oscillations and Simple Harmonic Motion (SHM)

• Characteristics of oscillatory motion
• Mathematical description of SHM
• Amplitude, period, frequency, phase
• Energy in SHM
• Examples: mass-spring system, pendulum

10. Fluid Mechanics

10.1 Fluid Statics

• Pressure and Pascal’s principle
• Buoyancy and Archimedes’ principle

10.2 Fluid Dynamics

• Equation of continuity
• Bernoulli’s equation and applications
• Viscosity and laminar vs turbulent flow

End of Unit Outline