ClassPhys F2024 L05 NewtonLaws

All formulas involve vectors.
Projectile Motion:
- Horizontal motion: ( v_x = \text{const} )
- Vertical motion: ( a_y = g = \text{const} )
- Motion in both x and y directions is interconnected through time, resulting in a parabolic trajectory.

Kinematics: Study of motion without forces (idealized objects, no mass considered).
Dynamics: Study of forces causing motion of masses.
History of Motion Analysis:
- 17th century contributions:
  - Galileo: Free fall
  - Huygens: Collisions
- Newton's 'Principia' (1686): Summary of fundamental principles of forces.
Classical Newtonian Mechanics:
- Valid under normal conditions but limited in extreme scenarios (high velocities, very small particle scales).
- Introduces concepts needed for understanding later mechanics (Lagrange and Hamilton).

1st Law (Inertia):
- An object remains at rest or in uniform motion unless acted upon by an external force.
2nd Law (F = ma):
- Acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
3rd Law (Action-Reaction):
- For every action, there is an equal and opposite reaction.

Objects move with constant velocity in the absence of forces, including being at rest.
Concept of Inertia: The property of an object to resist changes in motion.
Friction: Recognized as a key force affecting motion.
Emphasizes that the natural state of motion is one of uniform straight line motion or rest.

Force causes acceleration: The relationship is governed by ( F = m \cdot a ).
Mass is a fundamental property that resists motion changes.
Weight: The force of gravity on a mass (( F_g = m g )).
Units: Force measured in Newtons (e.g., weight of 1 kg ≈ 10 N).
Recognizes that without net force, objects can still maintain constant velocity.

Momentum: Introduces mass times velocity, applicable in systems where mass changes (e.g., rockets).
Distinction between Contact and Non-Contact Forces:
- Contact forces involve direct interaction (push/pull).
- Non-contact forces operate at a distance, such as gravity.
Equation of motion: Describes the motion of an object based on forces acting on it.

Action-Reaction Example: Understand that forces exist in pairs and that they act on different objects.
Examples of forces: Weight forces, support forces on objects resting on each other.
States that objects move due to total net forces acting upon them, not forces exerted on themselves.

Discusses a scenario where a man pulls a block, emphasizing equal and opposite forces.
Introduction of Free Body Diagrams to visualize forces acting on an object for better understanding.

Idealized conditions for ropes used in mechanics (massless and non-elastic).
Discussion on tension within ropes and how it transmits forces throughout its length.

Explores how the acceleration of connected masses can be analyzed and understood through their interactions.
Highlights importance of verifying calculated results with extreme value checks.

Comparison between different reference frames and conditions for observing forces.
Good reference systems are those moving with constant velocity (inertial frames).
Virtual forces can be observed in accelerated frames.

Mechanics predict the behavior of macroscopic objects by setting up equations of motion.
Second part of the lecture will cover Lagrangian and Hamiltonian mechanics as alternatives to Newtonian mechanics for solving motion problems.

Overview of the four fundamental forces:
- Strong Force: Short distance (gluons)
- Weak Force: Short distance (W and Z bosons)
- Electromagnetic Force: Inversely proportional to distance (photons)
- Gravitational Force: Inversely proportional to distance (gravitons)
These forces underlie all interactions including magnetic, van der Waals, and elastic forces.

Recap of motion description, calculus, vector application, and Newton's laws.
Anticipation of a deeper exploration into special forces in mechanics, such as gravitational and frictional forces.