Copy of Dynamics NLM LectureOutline

2.1: Systems & Center of Mass

• Definition: System properties are determined by interactions among objects within.

• Modeling: If constituent properties aren’t crucial, treat the system as a single object.

• Interactions: Systems may interact with the environment, transferring energy or mass.

• Behavior: Individual objects may behave differently from the system's overall behavior.

• Internal Structure: Affects how we analyze the system; changes in external variables can alter substructure.

Center of Mass (CM)

• Definition: Average position of an object's parts, weighted by mass.

• Balancing Point: Where a force can be applied without causing rotation.

• Symmetrical Systems: Positioned along lines of symmetry; CM of two particles is closer to the more massive one.

• Modeling: Can simplify analysis by using a single point at CM instead of multiple particles.

Real-World Applications

• Object Motion: Diver's motion represents translation and potential rotation.

• Experimental Finding: CM can be experimentally identified through suspension.

• Human Body Example: CM percentages for body parts help understand stability and movement.

2.2: Forces & Free-Body Diagrams

• Definition of Force: Vector quantities describing interactions; cannot exert a net force on itself.

  • Contact Forces: Interaction through physical contact (e.g., friction, normal, applied).

  • Field Forces: Act at a distance (e.g., gravitational).

Types of Forces

• Normal Force (FN): Perpendicular force during contact.

• Free-Body Diagrams (FBDs): Visual tools to analyze forces acting on an object.

  • Purpose: Isolate one object and explore interactions.

  • Steps to Create FBD: Identify the system's boundaries, interacting objects, and force directions.

  • Draw arrows representing force magnitude and direction, keeping in mind that arrows should originate from the center of mass.

2.3: Newton's Third Law

• Law Statement: For every action, there is an equal and opposite reaction.

• Force Interaction: Forces are exerted between different objects, maintaining equality in magnitude and opposite directions.

• Application Example: Rocket propulsion; exhaust gases expelled lead to movement upward.

2.4: Newton’s First Law (Law of Inertia)

• Definition: Objects in motion stay in motion at constant velocity unless acted upon by a net external force.

• Equilibrium Criterions: Any mass at rest or at a constant velocity experiences balanced forces.

2.5: Newton’s Second Law

• Basic Concept: Relation between force, mass, and acceleration; F = ma.

• Characteristics: Frame of Reference: Forces are vector quantities that can be analyzed along axes (ΣF = ma).

• Review: Acceleration indicates how velocity changes over time related to unbalanced forces.

2.6: Gravitational Force

• Formula: F_g = G(M1*M2)/r², where G is the gravitational constant.

• Mass vs. Weight: Mass is a measure of matter (in kg); weight is the force due to gravity (in Newtons).

• Inertial vs. Gravitational Mass: Gravitational mass (force of gravity) vs. inertial mass (resistance to acceleration).

Gravitational Interactions

• Objects experience gravitational pull towards larger masses.

• Normal Force: Counteracts weight; balances the force of gravity on surfaces.

2.7: Kinetic & Static Friction

• Friction Defined: Resistance to motion between two surfaces.

• **Types:

  • Static Friction: Prevents motion between surfaces at rest; variable force.

  • Kinetic Friction: Resistance during sliding motion; less than static.

• Applications: Static friction acts until limits are reached; coefficient of friction (μ) varies.

2.8: Spring Force

• Formula: F_s = -kx, where k is the spring constant.

• Behavior: Springs exert a restoring force opposite the direction of stretch or compression.

2.9: Circular Motion

• Fundamentals: Centripetal force acts toward the center to maintain circular motion.

• Acceleration Relationships: Centripetal acceleration is influenced by object speed and radius (a_r = v²/r).

• Frequency and Period: T = 1/f; frequency relates to the number of cycles per time unit.