AP Physics 1 Reference Sheet: Constants, Formulas, and Key Concepts

Constants and Conversion Factors

Fundamental Physical Constants

Physics relies on several universal constants and conversion factors for calculations in mechanics, fluids, and other domains. These constants are essential for solving problems and understanding physical relationships.

• Universal Gravitational Constant (G): $G = 6.67 \times 10^{-11} \ \mathrm{N \cdot m^2 / kg^2}$

• Acceleration due to gravity at Earth's surface (g): $g = 9.8 \ \mathrm{m/s^2}$

• Magnitude of the gravitational field strength at Earth's surface: $g = 9.8 \ \mathrm{N/kg}$

Unit Prefixes: Prefixes are used to express quantities in powers of ten.

Prefix	Symbol	Value
nano	n	$10^{-9}$
micro	μ	$10^{-6}$
milli	m	$10^{-3}$
centi	c	$10^{-2}$
kilo	k	$10^{3}$
mega	M	$10^{6}$

Unit Symbols: Common units in physics include:

Unit	Symbol
meter	m
kilogram	kg
second	s
ampere	A
kelvin	K
mole	mol

Trigonometric Functions for Common Angles

Values of Sine, Cosine, and Tangent

Trigonometric functions are frequently used in physics to resolve vectors and analyze motion.

Angle (degrees)	Angle (radians)	$\sin \theta$	$\cos \theta$	$\tan \theta$
0°	0	0	1	0
30°	$\pi/6$	$1/2$	$\sqrt{3}/2$	$1/\sqrt{3}$
45°	$\pi/4$	$1/\sqrt{2}$	$1/\sqrt{2}$	1
60°	$\pi/3$	$\sqrt{3}/2$	$1/2$	$\sqrt{3}$
90°	$\pi/2$	1	0	undefined

Geometry and Trigonometry in Physics

Area and Volume Formulas

Geometric formulas are used to calculate areas and volumes, which are important in mechanics and fluids.

• Rectangle: Area $A = l \times w$

• Triangle: Area $A = \frac{1}{2} b h$

• Circle: Area $A = \pi r^2$

• Sphere: Volume $V = \frac{4}{3} \pi r^3$

• Cylinder: Volume $V = \pi r^2 h$

Right Triangle Trigonometry:

• $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

• $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

• $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

Mechanics and Fluids: Symbols and Equations

Common Symbols in Physics

Symbols are used to represent physical quantities in equations. Understanding these is essential for interpreting formulas.

• a: acceleration

• F: force

• d: distance

• v: velocity

• m: mass

• p: momentum

• KE: kinetic energy

• PE: potential energy

• W: work

• P: power

• t: time

• g: acceleration due to gravity

• μ: coefficient of friction

Key Equations in Mechanics

These equations are foundational for solving problems in kinematics, dynamics, energy, and fluids.

• Kinematic Equations (constant acceleration):

  • $v = v_0 + a t$

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

  • $v^2 = v_0^2 + 2 a (x - x_0)$

• Newton's Second Law: $F = m a$

• Weight: $W = m g$

• Friction: $f = \mu N$

• Work: $W = F d \cos \theta$

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

• Potential Energy (gravitational): $PE = m g h$

• Conservation of Energy: $E_{\text{initial}} = E_{\text{final}}$

• Momentum: $p = m v$

• Impulse: $J = F \Delta t = \Delta p$

• Pressure (fluids): $P = \frac{F}{A}$

• Density: $\rho = \frac{m}{V}$

Example Applications

• Projectile Motion: Use kinematic equations to find range, maximum height, and time of flight.

• Inclined Plane: Resolve forces using trigonometric functions and Newton's laws.

• Conservation of Momentum: Analyze collisions using $m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$.

Summary Table: Key Equations and Their Applications

Equation	Physical Meaning	Application
$F = m a$	Newton's Second Law	Relates force, mass, and acceleration
$W = F d \cos \theta$	Work	Calculates work done by a force
$KE = \frac{1}{2} m v^2$	Kinetic Energy	Energy due to motion
$PE = m g h$	Potential Energy	Energy due to position in a gravitational field
$p = m v$	Momentum	Product of mass and velocity
$P = \frac{F}{A}$	Pressure	Force per unit area in fluids
$\rho = \frac{m}{V}$	Density	Mass per unit volume

Additional info:

• This reference sheet is designed for AP Physics 1 and covers foundational topics in mechanics and fluids, which align with college-level introductory physics courses.

• Students should be familiar with the use of these equations and constants in problem-solving and conceptual understanding.