Advanced Placement Physics C: Constants, Conversions, and Equations, Lecture notes of Physics

Download Advanced Placement Physics C: Constants, Conversions, and Equations and more Lecture notes Physics in PDF only on Docsity! 1 ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS Proton mass, mp = 1.67 x 10-27 kg Neutron mass, mn = 1.67 x 10-27 kg Electron mass, me = 9.11 x 10-31 kg Avogadro’s number, 𝑁! = 6.02 𝑥 10!"mol!! Universal gas content, 𝑅 = 8.31 J/ mol • K) Boltzmann’s constant, 𝑘! = 1.38 ×10!!"J/K Electron charge magnitude, e = 1.60 x 10-19 C 1 electron volt, 1 eV = 1.60 × 10!!" J Speed of light, c = 3.00 x 108 m/s Universal gravitational constant, G = 6.67 x 10- 11 m3/kg•s2 Acceleration due to gravity at Earth’s surface, g = 9.8 m/s2 1 unified atomic mass unit, 1 u = 1.66 × 10!!" kg = 931 MeV/𝑐! Planck’s constant, ℎ = 6.63 × 10!!" J • s = 4.14 × 10!!" eV • s ℎ𝑐 = 1.99 × 10!!" J •m = 1.24 × 10! eV • nm Vacuum permittivity, 𝜀! = 8.85 × 10!!" C!/(N •m!) Coulomb’s law constant, k = 1/4π𝜀0 = 9.0 x 109 N•m2/C2 Vacuum permeability, 𝜇! = 4𝜋 × 10!! (T •m)/A Magnetic constant, 𝑘‘ = !! !! = 1 × 10!! (T •m)/A 1 atmosphere pressure, 1 atm = 1.0 × 10! ! !! = 1.0 × 10! Pa UNIT SYMBOLS meter, m mole, mol watt, W farad, F kilogram, kg hertz, Hz coulomb, C tesla, T second, s newton, N volt, V degree Celsius, ˚C ampere, A pascal, Pa ohm, Ω electron volt, eV kelvin, K joule, henry, H VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES 𝜃 0˚ 30˚ 37˚ 45˚ 53˚ 60˚ 90˚ sin𝜃 0 1/2 3/5 2/2 4/5 3/2 1 cos𝜃 1 3/2 4/5 2/2 3/5 1/2 0 tan𝜃 0 3/3 ¾ 1 4/3 3 ∞ PREFIXES Factor Prefix Symbol 109 giga G 106 mega M 103 kilo k 10-2 centi c 10-3 milli m 10-6 micro 𝜇 10-9 nano n 10-12 pico p 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS Equation Usage a = acceleration E = energy F = force f = frequency h = height I = rotational inertia J = impulse K =kinetic energy k = spring constant ℓ = length L = angular momentum m = mass P =power p = momentum r = radius or distance T = period t = time U = potential energy V = volume v = velocity or speed W = work done on a system x = position 𝜇 = coefficient of friction 𝜃 = angle 𝜏 = torque 𝜔 = angular speed 𝛼 = angular acceleration 𝜙 = phase angle 𝑣! = 𝑣!! + 𝑎!𝑡 𝑥 = 𝑥! + 𝑣!!𝑡 + 1 2 𝑎!𝑡! 𝑣!! = 𝑣!!! + 2𝑎!(𝑥 − 𝑥!) Kinematic relationships for an object accelerating uniformly in one dimension. Can be applied in both x and y directions. 𝑎 = Σ𝐹 𝑚 = 𝐹!"# 𝑚 𝑎 = Σ𝜏 𝐼 = 𝜏!"# 𝐼 Newton’s second law. Newton’s second law for rotation. 𝐹 = 𝑑𝑝 𝑑𝑡 The total momentum of the system is the vector sum of the momenta of the individual objects. The rate of change of momentum is equal to the net external force. 𝐽 = 𝐹𝑑𝑡 = Δ𝑝 Impulse is defined as the average force acting over a time interval. Impulse is also equivalent to the change in momentum of the object receiving the impulse. 𝑝 = 𝑚𝑣 Defines momentum for a single object moving with some velocity. 𝐹! ≤ 𝜇 𝐹! The relationship for the frictional force acting on an object on a rough surface. ΔΕ = 𝑊 = 𝐹 • 𝑑𝑟 Calculate the work done on an object by a force 𝐾 = 1 2 𝑚𝑣! The definition of kinetic energy. 𝑃 = 𝑑𝐸 𝑑𝑡 Defines power. 𝑃 = 𝐹 • 𝑣 Defines power. Δ𝑈! = 𝑚𝑔Δℎ The definition of the gravitational potential energy of a system consisting of the Earth and on object of mass m near the surface of the Earth. 𝑎! = 𝑣! 𝑟 = ω!𝑟 Centripetal acceleration Angular velocity 𝜏 = 𝑟 × 𝐹 The definition of torque. 𝛪 = 𝑟!𝑑𝑚 = Σ𝑚𝑟! The general definition of moment of inertia. The calculus definition of moment of 5 The electrical potential energy stored in a capacitor. 𝑅 = 𝜌ℓ 𝐴 The definition of resistance in terms of the properties of the conductor. 𝐸 = 𝜌𝐽 The relationship that defines current density (current per cross-sectional area) in a conductor. 𝐼 = 𝑁𝑒𝑣!𝐴 The definition of current in a conductor. 𝐼 = ∆𝑉 𝑅 Ohm’s Law 𝑅! = 𝑅! ! The rule for equivalent resistance for resistors arranged in series. 1 𝑅! = 1 𝑅!! The rule for equivalent resistance for resistors arranged in parallel. 𝑃 = 𝐼∆𝑉 The definition of power or the rate of heat loss through a resistor. 𝐹! = 𝑞𝑣 × 𝐵 The magnetic force of interaction between a moving charged particle and a uniform magnetic field. 𝐵 • 𝑑ℓ = 𝜇!𝐼 Ampère’s Law (a fundamental law of magnetism that relates the magnitude of the magnetic field to the current enclosed by a closed imaginary path called an Amperian loop) in integral form. 𝑑𝐵 = 𝜇! 4𝜋 𝐼𝑑ℓ×𝑟 𝑟! The Biot-Savart Law (the fundamental law of magnetism that defines the magnitude and direction of a magnetic field due to moving charges or current-carrying conductors in differential form 𝐹 = 𝐼𝑑ℓ × 𝐵 The definition of the magnetic force acting on a straight-line segment of a current-carrying conductor in a uniform magnetic field. 𝐵! = 𝜇!𝑛𝐼 Can be used to determine the magnetic field inside a solenoid. Φ! = 𝐵 • 𝑑𝐴 The definition of magnetic flux. 𝜀 = −𝐿 𝑑𝐼 𝑑𝑡 Faraday’s Law. 𝑈! = 1 2 𝐿𝐼! The stored energy in an inductor. 6 GEOMETRY AND TRIGONOMETRY Equation Usage A = bh Rectangle A = area C = circumference V = volume S = surface area b = base h = height ℓ = length w = width r = radius s = arc length 𝜃 = angle A = ! ! 𝑏ℎ Triangle 𝐴 = 𝜋𝑟! 𝐶 = 2𝜋𝑟 𝑠 = 𝑟𝜃 Circle 𝑉 = ℓ𝑤ℎ Rectangular Solid 𝑉 = 𝜋𝑟!ℓ 𝑆 = 2𝜋𝑟ℓ + 2𝜋𝑟! Cylinder 𝑉 = 4 3 𝜋𝑟! 𝑆 = 4𝜋𝑟! Sphere 𝑎! + 𝑏! = 𝑐! sinθ = 𝑎 𝑐 cosθ = 𝑏 𝑐 tanθ = 𝑎 𝑏 Right Triangle CALCULUS 𝑑𝑓 𝑑𝑥 = 𝑑𝑓 𝑑𝑢 𝑑𝑢 𝑑𝑥 𝑑 𝑑𝑥 𝑥! = 𝑛𝑥!!! 𝑑 𝑑𝑥 𝑒!" = 𝑎𝑒!" 𝑑 𝑑𝑥 ln 𝑎𝑥 = 1 𝑥 𝑑 𝑑𝑥 sin 𝑎𝑥 = 𝑎cos 𝑎𝑥 𝑑 𝑑𝑥 cos 𝑎𝑥 = −𝑎sin 𝑎𝑥 𝑥!𝑑𝑥 = 1 𝑛 + 1 𝑥!!!, 𝑛 ≠ −1 𝑒!"𝑑𝑥 = 1 𝑎 𝑒!" 𝑑𝑥 𝑥 + 𝑎 = 1𝑛 𝑥 + 𝑎 cos 𝑎𝑥 𝑑𝑥 = 1 𝑎 sin 𝑎𝑥 sin 𝑎𝑥 𝑑𝑥 = − 1 𝑎 cos 𝑎𝑥 VECTOR PRODUCTS 𝐴 • 𝐵 = 𝐴𝐵cosθ 𝐴 × 𝐵 = 𝐴𝐵sinθ 7 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.