Galileo's Law: "A body at rest remains at rest and a body in motion continues to move at constant velocity along a straight line unless acted upon by an external force."
Newton's Words (Principia): "Every body perseveres in its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed upon it."
Implications: Contradicts daily experiences due to factors like gravity and friction which are always present.
Inertial Frames: The First Law only holds in inertial reference frames (no acceleration).
Examples:
Non-inertial: Accelerating on a horse or bike.
Inertial: Theoretically possible where no accelerations exist (26.100 lecture hall is close to inertial despite Earth's rotations).
Newton's Second Law: F = ma
Experimental Fact: m1 * a1 = m2 * a2.
Definition of Force: ma (mass times acceleration).
Expression: "A force acting on a body gives it an acceleration in the direction of the force and has a magnitude given by ma."
Units: Newton, N (kilogram meter per second squared).
Inertial Frames Requirement: Valid in inertial reference frames.
Examples: Extending spring with different masses (m1, m2).
Statement: "If one object exerts a force on another, the other exerts the same force in the opposite direction on the one."
Simplified: Action = - Reaction.
Examples:
Sitting on a chair: You push down, chair pushes up.
Holding a baseball: Hand pushes on the ball, ball pushes on the hand.
Hero's Engine and Rocket Principle.
Application and Examples
Block on Two Strings: Analyzing tensions in strings holding a 2 kg block.
Hero's Engine: Demonstrates action-reaction principle through steam ejection.
Rocket Principle: Behavior of balloons and garden hoses.
Ball Falling Towards Earth: Even minute movements of Earth due to a falling object demonstrate equal and opposite reactions.
Key Insights
Non-Intuitive Results: Sometimes experimental results seem counterintuitive, hence multiple trials and verifications are essential.
High-Energy/Momentum Cases: When speeds approach the speed of light, relativistic mechanics (Einstein's Theory) must be used.
Importance of Verification: Consistency with experimental evidence is critical to the validation of physical laws.
Conclusion
Understanding and applying Newton's Laws requires recognizing inertial vs. non-inertial frames, verifying through experiments, and realizing the broader implications of seemingly simple principles.