Advanced Placement Physics 2 Table of Information

ADVANCED PLACEMENT PHYSICS 2 TABLE OF INFORMATION

CONSTANTS AND CONVERSION FACTORS Proton mass, mp = 1.67 x 10-27 kg Electron charge magnitude, e = 1.60 x 10-19 C

!!" Neutron mass, mn = 1.67 x 10-27 kg 1 electron volt, 1 eV = 1.60 × 10 J

Electron mass, me = 9.11 x 10-31 kg Speed of light, c = 3.00 x 108 m/s

!" !! - Avogadro’s number, �! = 6.02 � 10 mol Universal gravitational constant, G = 6.67 x 10 11 m3/kg•s2 Universal gas constant, � = 8.31 J/ mol • K) Acceleration due to gravity at Earth’s surface, g !!" 2 Boltzmann’s constant, �! = 1.38 ×10 J/K = 9.8 m/s 1 unified atomic mass unit, 1 u = 1.66 × 10!!" kg = 931 MeV/�!

Planck’s constant, ℎ = 6.63 × 10!!" J • s = 4.14 × 10!!" eV • s ℎ� = 1.99 × 10!!" J • m = 1.24 × 10! eV • nm

!!" ! ! Vacuum permittivity, �! = 8.85 × 10 C /(N • m )

Coulomb’s law constant, k = 1/4π�0 = 9.0 x 109 N•m2/C2

!! Vacuum permeability, �! = 4� × 10 (T • m)/A

! Magnetic constant, �‘ = ! = 1 × 10!! (T • m)/A !!

! 1 atmosphere pressure, 1 atm = 1.0 × 10! = 1.0 × 10! Pa !!

meter, m mole, mol watt, W farad, F kilogram, kg hertz, Hz coulomb, C tesla, T UNIT SYMBOLS second, s newton, N volt, V degree Celsius, ˚C ampere, A pascal, Pa ohm, Ω electron volt, eV kelvin, K joule, henry, H

PREFIXES Factor Prefix Symbol VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES 10!" tera T � 0˚ 30˚ 37˚ 45˚ 53˚ 60˚ 90˚ 109 giga G sin� 0 1/2 3/5 4/5 1 106 mega M 2/2 3/2 103 kilo k cos� 1 3/2 4/5 2/2 3/5 1/2 0 10-2 centi c tan� 0 3/3 ¾ 1 4/3 3 ∞ 10-3 milli m 10-6 micro � 10-9 nano n 10-12 pico p

1 ADVANCED PLACEMENT PHYSICS 2 EQUATIONS

MECHANICS Equation Usage �! = �!! + �!� Kinematic relationships for an object accelerating uniformly in one 1 dimension. Can be applied in both x and � = � + � � + � �! ! !! 2 ! y directions. a = acceleration ! ! �! = �!! + 2�!(� − �!) A = amplitude d = distance Σ� � Force exerted on an object due to the E = energy � = = !"# � � interaction of that object with another F = force object. f = frequency I = rotational inertia Σ� �!"# � = = K =kinetic energy � � k = spring constant � = �� Defines momentum for a single object L = angular momentum moving with some velocity. ℓ = length m = mass ∆� = �∆� Average change in momentum or impulse P =power p = momentum �! ≤ � �! The relationship for the frictional force acting on an object on a rough surface. r = radius or separation T = period � = � � Static friction ! t = time 1 ! Elastic/spring potential energy �! = �� U = potential energy 2 v = speed 1 The definition of kinetic energy. � = ��! W = work done on a system 2 x = position Δ� = � = � � = �� Energy transfer ∥ y = height Δ� Power is defined as the rate of energy � = � = angular acceleration Δ� transfer into, out of, or within a system. � = coefficient of friction Δ�! = ��Δ� Gravitational potential energy � = angle �! Centripetal acceleration � = torque � = ! � Angular velocity � = angular speed � = �!� = ��sin� The definition of torque. !�! Calculate the center of mass for a �!" = �! nonuniform solid that can be considered as a collection of regular masses or for a system of masses. 1 Kinetic energy in a rotating object. � = ��! 2 1 The angular kinematic relationships for � = � + � � + ��! ! ! 2 objects experiencing a uniform angular � = �! + �� acceleration. � = �� A simple wave can be described by an = ��(2��) equation involving one sine or cosine function involving the wavelength, amplitude, and frequency of the wave. � = �� Angular momentum

2 ∆� = �∆� 2� 1 The period of simple harmonic motion � = = � � (SHM) is related to the angular frequency. � The period of a system oscillating in � = 2� ! � simple harmonic motion (SHM), or its equivalent for a pendulum or physical pendulum, and this can be shown to be � �! = 2� true experimentally from a plot of the � appropriate data.

�!�! The magnitude of the gravitational �! = � �! force between two masses can be determined by using Newton’s universal law of gravitation.

�! Gravitational force � = � �� The gravitational potential energy of the object-Earth system (shown � = − ! ! ! � using the relationship between the conservative force and potential energy.

ELECTRICITY AND MAGNETISM Equation Usage 1 �!�! Coulomb’s Law; gives the A = area �! = ! 4��! � magnitude of electromagnetic B = magnetic field force between two point C = capacitance charges. d = distance E = electric field �! The definition of electric field. � = ℇ = emf � F = force 1 � Gives the magnitude of the � = I = current ! electric field at a distance from 4��! � ℓ = length the center of a source object of P = power electric charge. Q = charge ∆� = �∆� Changes in a system’s internal ! q = point charge structure can result in changes R = resistance in internal energy. r = separation � Calculate magnitude of an � = t = time electric field between two �!� U = potential or stored energy oppositely charged parallel V = electric potential plates with uniformly v = speed distributed electric charge. � = dielectric constant ∆� The average value of the � = � = resistivity electric field in a region ∆� � = angle

Φ = flux

3 � � Magnitude of a magnetic field � = ! 2� � �! = �� ×� The magnetic force of interaction between a moving charged particle and a uniform magnetic field.

�! = �� sin� � The magnetic force depends on the angle between the velocity and the magnetic field vectors.

�! = �ℓ × � A magnetic force results from the interaction of a moving charged object or a magnet with other moving charged objects or another magnet.

�! = �ℓ sin� � The force exerted on a moving charged object is perpendicular to both the magnetic field and the velocity of the charge and is described by a right-hand rule. 1 � Isolines � = 4��! � Φ! = � • � Changing magnetic flux

Φ! = � cosθ �

� = �ℓ�

∆Φ � = − ! ∆� � Calculates the energy stored in a capacitor. ∆� = � �� Calculates the capacitance of a parallel-plate capacitor with a � = ! � dielectric material inserted between the plates. � = � Can be used to determine the equivalent capacitance of ! ! capacitors arranged in parallel. ! 1 1 Can be used to determine the equivalent capacitance of = �! �! capacitors arranged in series. ! ∆� An electrical current is a movement of charge through a � = ∆� conductor. 1 1 The energy stored in a capacitor. � = �∆� = �(∆�)! ! 2 2 The electrical potential energy stored in a capacitor. �ℓ The definition of resistance in terms of the properties of the � = � conductor. ∆� Ohm’s Law � = � The rule for equivalent resistance for resistors arranged in series. �! = �! ! 1 1 The rule for equivalent resistance for resistors arranged in = �! �! parallel. ! � = �∆� The definition of power or the rate of heat loss through a resistor.

FLUID PHYSICS AND THERMAL MECHANICES EQUATION USAGE � � = Calculate density �

4 � Calculate force A = area � = � F = force h = depth � = �! + ��ℎ Calculate absolute pressure k = thermal conductivity K = kinetic energy �! = ��ℎ Calculate contact force L = thickness m = mass �!�! = �!�! Continuity equation (used to n = number of moles describe conservation of mass N = number of molecules flow rate in fluids) P = pressure 1 Bernoulli’s equation (describes Q = energy transferred to a � + �� + ��! ! ! 2 ! the conservation of energy in system by heating 1 fluid flow) T = temperature = � + �� + ��! ! ! 2 ! Calculate pressure t = time U = internal energy V = volume � ��∆� Thermal conductivity is the v = speed = ∆� � measure of a material’s ability W = work done on a system to transfer thermal energy. y = height �� = �� − ��!� The ideal gas law � = density

3 Calculate the average kinetic � = � � 2 ! energy of a system

� = −�∆� Defines the work done on a system. ∆� = � + � Change in internal energy of a system involves the possible transfer of energy through work and/or heat.

WAVES AND OPTICS EQUATION USAGE d = separation � � = Wavelength f = frequency or focal length � h = height � � = Refraction L = distance � M = magnification �!sin�! = �!sin�! Snell’s Law m = an integer 1 1 1 Law of reflection + = n = index of refraction �! �! � s = distance ℎ! �! v = speed � = = ℎ! �! � = wavelength ∆� = �� Diffraction � = angle

�sin� = ��

MODERN PHYSICS EQUATION USAGE E = energy

5 � = ℎ� Energy of a photon F = frequency �!"# = ℎ� − � Photoelectric effect K = kinetic energy ℎ Wavelength of a particle m = mass � = � p = momentum � = ��! Equation derived from the � = wavelength theory of special relativity. � = work function

GEOMETRY AND TRIGONOMETRY Equation Usage A = bh Area of a rectangle A = area ! A = �ℎ Area of a triangle C = circumference ! V = volume � = ��! Area of a circle S = surface area Circumference of a circle � = 2�� b = base � = ℓ�ℎ Volume of a rectangular solid ! h = height � = �� ℓ Volume of a cylinder ℓ = length ! � = 2��ℓ + 2�� Surface area of a cylinder � = width 4 Volume of a sphere � = ��! r = radius 3 Surface area of a sphere � = 4��! Pythagorean theorem Calculate the value of the �! = �! + �! � angles of a right triangle sinθ = � � cosθ = � � tanθ = �

The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges would drift. III. The electric potential is zero at an infinite distance from an isolated point charge. IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated.