Mechanics Flashcards | IB - Wyatt's Notes
Mechanics Flashcards
20 flashcards covering IB Physics mechanics — kinematics, dynamics, work and energy, momentum, and circular motion.
Key Concepts
Newton’s Laws of Motion: First law (inertia): an object remains at rest or in uniform motion unless acted upon by a resultant force. Second law: F = ma (the resultant force equals mass times acceleration). Third law: for every action, there is an equal and opposite reaction (forces always come in pairs acting on different objects). These laws form the foundation of classical mechanics and apply in all inertial reference frames.
Work, Energy, and Power: Work done = Force × displacement × cosθ (W = Fs cosθ), where θ is the angle between force and displacement. Kinetic energy = ½mv². Gravitational potential energy = mgh. The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Power = work done / time = force × velocity. Energy is conserved in closed systems — it can be transferred between forms but cannot be created or destroyed.
Momentum and Impulse: Momentum p = mv (mass × velocity). Impulse = Force × time = change in momentum (FΔt = Δp). In collisions, total momentum is conserved if no external forces act. Elastic collisions conserve both momentum and kinetic energy; inelastic collisions conserve momentum but not kinetic energy. In a perfectly inelastic collision, the objects stick together.
Circular Motion: An object moving in a circle at constant speed is accelerating because its direction changes continuously. Centripetal acceleration = v²/r directed toward the centre. Centripetal force = mv²/r. This force is provided by different mechanisms in different contexts: gravity for orbits, friction for cars on roads, tension for pendulums, electrostatic force for electrons orbiting nuclei.
Intuition
Mechanics is the branch of physics that describes motion and its causes. Kinematics describes how things move (displacement, velocity, acceleration) without worrying about why. Dynamics explains why through Newton’s laws — forces cause acceleration, and every action has an equal and opposite reaction. Energy conservation provides a powerful shortcut: instead of tracking forces through complex paths, you can compare initial and final energy states directly. Momentum is a “conserved quantity” — it’s the physics equivalent of “what goes around comes around.”
Why it matters: Mechanics is the foundation of all physics. Understanding forces, energy, and momentum is essential for engineering, sports science, aerospace, and any field involving motion. It teaches systematic problem-solving and the power of conservation laws.
Common Pitfalls
- Sign errors in kinematics: Forgetting that velocity and acceleration are vectors — if you define “up” as positive, gravity (acting down) must be negative in your equations. A common error is mixing signs within one problem, which gives incorrect answers.
- Normal force confusion: The normal force is not always equal to mg — on an incline, it equals mg cos θ; in accelerating elevators, it changes with the acceleration. The normal force adjusts to prevent objects from passing through surfaces.
- Momentum in explosions: Forgetting that momentum is conserved in all directions independently — a system can have zero total momentum in one direction while having non-zero momentum in another. Always analyse x and y components separately.
- Confusing elastic and inelastic collisions: Both conserve momentum, but only elastic collisions conserve kinetic energy. In inelastic collisions, kinetic energy is converted to heat, sound, or deformation.
Cross-References
- Kinematics: Kinematics describes motion without explaining its causes — mechanics provides the causal explanation through forces and energy.
- Waves: Waves transfer energy, and mechanical waves (sound, water waves) involve oscillating particles governed by mechanical principles.
- Thermal Physics: Thermal physics explains how mechanical energy converts to internal energy through friction and heat transfer.
- Electricity: Electric forces cause charges to accelerate, and circuit analysis uses energy conservation principles from mechanics.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.
Advanced Content
This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.
Derivations and Proofs
Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.
Extended Examples
Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.
Research Connections
This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.
Prerequisites
Ensure you have mastered the prerequisite material before attempting this advanced content.