Translational Motion

Kinematics and Dynamics

This section covers the fundamental equations describing the motion of objects in a straight line, including displacement, velocity, acceleration, and Newton's laws.

• Displacement:

• Velocity:

• Average Velocity:

• Displacement (from velocities):

• Newton's Second Law:

• Friction Force:

• Work:

• Kinetic Energy:

• Potential Energy (gravity):

• Work-Energy Theorem:

• Power:

Rotational Motion

Angular Kinematics and Dynamics

Describes the motion of rotating bodies, including angular displacement, velocity, acceleration, and the rotational analogs of Newton's laws.

• Angular Displacement:

• Angular Velocity:

• Average Angular Velocity:

• Angular Displacement (from velocities):

• Torque:

• Moment of Inertia (discrete):

• Moment of Inertia (continuous):

• Rotational Kinetic Energy:

• Angular Momentum:

Elasticity

Stress, Strain, and Moduli

Elasticity describes how materials deform under applied forces and return to their original shape when the forces are removed.

• Young's Modulus:

• Shear Modulus:

• Bulk Modulus:

Fluid Mechanics

Fluid Statics

Fluid statics deals with fluids at rest and the forces and pressures associated with them.

• Pressure:

• Hydrostatic Pressure:

• Buoyant Force:

• Pascal's Principle:

Fluid Dynamics

Fluid dynamics studies fluids in motion, including the conservation of mass and energy in flowing fluids.

• Equation of Continuity:

• Bernoulli's Equation:

• Poiseuille's Law (cylinder):

Thermal Motion of Molecules

Kinetic Theory and Gas Laws

This section explains the microscopic behavior of gases, relating temperature to molecular motion and energy.

• Pressure (kinetic theory):

• Root Mean Square Speed:

• Ideal Gas Law:

• Boltzmann Constant:

Heat

Heat Transfer and Calorimetry

Describes the transfer of thermal energy, specific heat, and phase changes.

• Heat Transfer:

• Latent Heat:

• Heat Conduction:

• Stefan-Boltzmann Law:

Material Properties

Physical Properties of Substances

Lists important physical constants and properties for common materials, useful for calculations in mechanics, fluids, and heat.

Numerical Constants & Conversions

Fundamental Constants

• Gravitational Acceleration: m/s

• Universal Gas Constant: J/mol·K

• Avogadro's Number: mol

• Boltzmann Constant: J/K

Extras

Quadratic Equation

• General Solution: