Core Concepts in College Physics

Derivatives and Kinematics

Kinematics is the study of motion without considering its causes. It involves the use of derivatives to relate position, velocity, and acceleration.

• Position, Velocity, and Acceleration:

  • Velocity:

  • Acceleration:

  • Displacement:

• Constant Acceleration Equations:

• Projectile Motion: Motion in two dimensions under constant acceleration due to gravity.

Integrals and Length

Integrals are used to calculate quantities such as area, displacement, and length in physics.

• Definite Integral:

• Arc Length:

Vectors and Other Math

Vectors are quantities with both magnitude and direction, essential for describing physical phenomena.

• Vector Addition:

• Dot Product:

• Cross Product:

Dynamics: Force and Motion

Dynamics studies the relationship between motion and the forces causing it, primarily through Newton's Laws.

• Newton's Second Law:

• Friction:

• Gravitational Force:

Work and Energy

Work and energy are central concepts in physics, describing how forces cause changes in motion and how energy is transferred.

• Work:

• Kinetic Energy:

• Potential Energy (Gravity):

• Work-Energy Theorem:

Oscillations

Oscillatory motion occurs when an object moves back and forth about an equilibrium position.

• Simple Harmonic Motion (SHM):

  • Period:

  • Frequency:

  • Angular Frequency:

Fundamental Constants and Physical Properties

Physics relies on fundamental constants and properties for calculations and understanding natural laws.

• Examples of Constants:

  • Speed of light: m/s

  • Gravitational constant: N m/kg

  • Planck's constant: J s

  • Elementary charge: C

  • Mass of electron: kg

  • Mass of proton: kg

  • Earth's radius: m

Rotational Motion: Moments of Inertia

The moment of inertia quantifies an object's resistance to rotational acceleration about an axis.

Additional info:

• Some equations and constants are inferred from standard physics curriculum and the visible formula sheet.

• Images referenced in the table are described for context; actual images are not included.