AP Physics C Mechanics Review Lecture

Introduction

• Review of all content learned in mechanics for AP Physics C.
• Focus on rapid review of key concepts without interaction.

Basic Concepts

Vector vs Scalar

• Vector: Has both magnitude and direction.
• Scalar: Has only magnitude.
• Important for problems like momentum (a vector) in conservation problems.

Uniformly Accelerated Motion (UAM)

• Used when acceleration is constant.
• Equations: Four key UAM equations (typically three given, but fourth can be used).
• Variables: Five UAM variables.
• Knowing three variables allows calculation of the others.

Acceleration

• Instantaneous Acceleration: Derivative of velocity w.r.t. time.
• Average Acceleration: Change in velocity over change in time.
• Velocity calculated as integral of acceleration over time.
• Position: Integral of velocity over time.
• Derivatives and Integrals: Derivative = slope; Integral = area under curve.

Projectile Motion

• X-direction: Net force zero, constant velocity.
• Y-direction: Acceleration = -g (free fall condition).
• Time: Scalar and direction-independent.

Newton's Laws and Forces

Newton's Second Law

• Derivative Formulation: Net force = derivative of momentum w.r.t. time.
• Momentum: Usually assume constant mass, simplifying to F = ma.

Impulse

• Symbol: J.
• Relation: Impulse = integral of force w.r.t. time = change in momentum.

Conservation of Momentum

• If net force is zero, momentum conserved (initial = final momentum).

Forces

• Friction: Less than or equal to μ times normal force.
  • Static Friction: Adjusts to prevent motion.
  • Kinetic Friction: Opposes motion.
• Direction: Generally opposes motion but can vary in complex systems (e.g., truck example).

Energy Concepts

Work

• Work = Integral of force dot product with position.
• Work = F * r * cos(θ) for constant force.

Mechanical Energy

• Types: Kinetic, Gravitational Potential, Elastic Potential.
• Equations:
  • Conservation of Mechanical Energy (no friction or external forces).
  • Work due to friction = change in mechanical energy.
  • Net work equals change in kinetic energy.

Power

• Power = Derivative of work w.r.t. time.
• Power = Force dot velocity for constant force.

Conservative Forces

• Conservative Force Equation: Force = negative derivative of potential energy.
• Example: Spring force calculated from potential energy.

Center of Mass

• System of Particles: Calculation based on weighted positions over total mass.
• Rigid Object: Integral form using position and mass distribution.
• Derivative Applications: Can calculate velocity and acceleration of center of mass.

Conclusion

• Lecture notes available at FlippingPhysics.com for detailed reference.