Comprehensive Physics Formula Sheet: Mechanics, Fluids, Heat, and Material Properties

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: $x = x_0 + v_0 t + \frac{1}{2} a t^2$

• Velocity: $v = v_0 + a t$

• Average Velocity: $v_{avg} = \frac{v + v_0}{2}$

• Displacement (from velocities): $x = x_0 + v_{avg} t$

• Newton's Second Law: $\sum \vec{F} = m \vec{a}$

• Friction Force: $f = \mu N$

• Work: $W = F d \cos \theta$

• Kinetic Energy: $K = \frac{1}{2} m v^2$

• Potential Energy (gravity): $U_g = mgh$

• Work-Energy Theorem: $W_{net} = \Delta K$

• Power: $P = \frac{dW}{dt}$

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: $\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2$

• Angular Velocity: $\omega = \omega_0 + \alpha t$

• Average Angular Velocity: $\omega_{avg} = \frac{\omega + \omega_0}{2}$

• Angular Displacement (from velocities): $\theta = \theta_0 + \omega_{avg} t$

• Torque: $\tau = r F \sin \theta$

• Moment of Inertia (discrete): $I = \sum m_i r_i^2$

• Moment of Inertia (continuous): $I = \int r^2 dm$

• Rotational Kinetic Energy: $K_{rot} = \frac{1}{2} I \omega^2$

• Angular Momentum: $L = I \omega$

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: $Y = \frac{F/A}{\Delta L / L_0}$

• Shear Modulus: $S = \frac{F/A}{\Delta x / h}$

• Bulk Modulus: $B = -\frac{\Delta P}{\Delta V / V_0}$

Fluid Mechanics

Fluid Statics

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

• Pressure: $P = \frac{F}{A}$

• Hydrostatic Pressure: $P = P_0 + \rho g h$

• Buoyant Force: $F_B = \rho_{fluid} V_{disp} g$

• Pascal's Principle: $\Delta P = \rho g \Delta h$

Fluid Dynamics

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

• Equation of Continuity: $A_1 v_1 = A_2 v_2$

• Bernoulli's Equation: $P + \frac{1}{2} \rho v^2 + \rho g y = \text{constant}$

• Poiseuille's Law (cylinder): $\Delta P = Q R$

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): $P = \frac{1}{3} \rho \overline{v^2}$

• Root Mean Square Speed: $v_{rms} = \sqrt{\frac{3k_B T}{m}}$

• Ideal Gas Law: $PV = nRT$

• Boltzmann Constant: $k_B = 1.381 \times 10^{-23} \text{ J/K}$

Heat

Heat Transfer and Calorimetry

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

• Heat Transfer: $Q = mc\Delta T$

• Latent Heat: $Q = mL$

• Heat Conduction: $Q = \frac{kA\Delta T}{d} t$

• Stefan-Boltzmann Law: $P = \sigma A T^4$

Material Properties

Physical Properties of Substances

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

Property	Value
Density (water)	$1.00 \times 10^3$ kg/m$^3$
Density (air)	$1.29$ kg/m$^3$
Surface tension (water)	$0.073$ N/m
Specific heat (water)	$4186$ J/kg·K
Latent heat of fusion (water)	$3.33 \times 10^5$ J/kg
Latent heat of vaporization (water)	$2.26 \times 10^6$ J/kg
Thermal conductivity (water)	$0.60$ W/m·K

Numerical Constants & Conversions

Fundamental Constants

• Gravitational Acceleration: $g = 9.80$ m/s$^2$

• Universal Gas Constant: $R = 8.314$ J/mol·K

• Avogadro's Number: $N_A = 6.02 \times 10^{23}$ mol$^{-1}$

• Boltzmann Constant: $k_B = 1.381 \times 10^{-23}$ J/K

Extras

Quadratic Equation

• General Solution: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$