AP Physics C Mechanics Lecture Notes

Overview

• Comprehensive review of AP Physics C Mechanics, covering all necessary topics for the exam:
  • Kinematics
  • Force and Translational Dynamics
  • Work and Power
  • Linear Momentum
  • Torque and Rotation
  • Energy and Momentum of Rotating Systems
  • Oscillations

Unit 1: Kinematics

Scalars vs. Vectors

• Scalars: Quantity with magnitude only (e.g., mass, distance).
• Vectors: Quantity with magnitude and direction (e.g., displacement, velocity).
• Vector Addition: Add x-components and y-components separately.

Vector Notation

• Graphical Representation: Arrows on axes.
• Component Notation: v = 3i + 6j + 0k.
• Magnitude Calculation: Pythagorean Theorem.

Displacement vs. Distance

• Displacement: Vector from start to end point.
• Distance: Total path length (scalar).

Position, Velocity, and Acceleration

• Position (x): Object's location.
• Velocity (v): Derivative of position; speed and direction.
• Acceleration (a): Derivative of velocity; rate of change of velocity.

Reference Frames

• Relative Motion: Calculating velocity relative to different frames.
• Constant Acceleration: Same across reference frames.

Projectile Motion

• 2D Motion: Decompose into horizontal and vertical components.
• Key Equations:
  • vx = v₀cosθ
  • vy = v₀sinθ
• Symmetrical Path: Time to apex = total time / 2.
• Acceleration:
  • Ax = 0
  • Ay = -g

Unit 2: Force and Translational Dynamics

Center of Mass

• Symmetrical Masses: COM lies on symmetry axes.
• System of Masses: Use
  • x_COM = (Σmx) / Σm
  • y_COM = (Σmy) / Σm

Newton’s Laws

• First Law: Object in motion stays in motion; at rest stays at rest.
• Second Law: ΣF = ma.
• Third Law: Action-reaction pairs are equal and opposite.

Types of Forces

• Gravitational (Fg): Fg = G(m₁m₂/r²).
• Normal Force (Fn): Perpendicular to surface.
• Frictional Force (Ff): Ff = μFn, opposing force.
• Spring Force (Fs): Fs = kx (Hooke's Law).
• Centripetal Force (Fc): Fc = mv²/r.

Drag and Terminal Velocity

• Drag Force: Opposes direction of motion; Fd = bv.
• Terminal Velocity: When drag force equals gravitational force.

Unit 3: Work, Energy, and Power

Types of Energy

• Kinetic Energy (K): K = 1/2 mv².
• Potential Energy (U):
  • Gravitational: Ug = mgh.
  • Spring: Us = 1/2 kx².

Work-Energy Theorem

• Work (W): Change in energy; W = ∫F·dx.
• Power (P): P = dW/dt; rate of doing work.

Conservation of Energy

• Mechanical Energy: KE + PE = constant.

Unit 4: Linear Momentum

Conservation of Momentum

• Momentum (p): p = mv.
• Impulse (J): Change in momentum; J = ∫F dt.
• Elastic vs Inelastic Collisions:
  • Elastic: KE conserved.
  • Inelastic: KE not conserved.

Unit 5: Torque and Rotational Dynamics

Rotational Kinematics

• Angular Quantities:
  • θ (angular displacement)
  • ω (angular velocity)
  • α (angular acceleration)

Torque (τ)

• Torque Equation: τ = r × F = Frsinθ.

Rotational Inertia

• Moment of Inertia (I): Resistance to rotational change; I = Σmr².

Calculating Rotational Inertia

• Parallel Axis Theorem: I = I_COM + Md².

Unit 6: Energy and Momentum of Rotating Systems

Rotational Kinetic Energy

• Equation: K_rotational = 1/2 Iω².

Angular Momentum

• Equation: L = Iω (for extended objects).
• Conservation of Angular Momentum: L_initial = L_final if no external torque.

Universal Gravitation

• Gravitational Force: Fg = G(m₁m₂/r²).
• Kepler’s Third Law: T² ∝ r³ (derivable).

Unit 7: Oscillations

Simple Harmonic Motion (SHM)

• Types: Mass-spring systems, pendulums.
• Period Equations:
  • Mass-Spring: T = 2π√(m/k)
  • Pendulum: T = 2π√(L/g)

Damped Oscillations

• Energy Dissipation: Amplitude decreases over time due to non-conservative forces.

Energy in SHM

• Equilibrium Position: Maximum kinetic energy.
• At Maximum Displacement: Maximum potential energy.

These notes provide a comprehensive overview of key concepts and equations needed for understanding AP Physics C Mechanics.