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Physics 117 Equation Sheet MECHANICS For constant acceleration, ax: (same for y-motion) Quadratic equation: Relative velocity: Dynamics: Friction: (kinetic), (static) For circular motion: Newton’s law of gravity: , Spring Force: Work: , Energy: (non-conservative) (kinetic energy), (gravitational potential energy) (spring potential energy) (Average) Power: , Momentum: STATICS Torque: , (impulse) (d=lever arm) Center of gravity (mass): FLUIDS (density) (pressure) Variation of pressure with depth in a static fluid: Archimedes’ principle: Equation of Continuity: Bernoulli’s equation: HEAT Thermal expansion: (linear), Conduction of heat: = rate of heat energy transfer Stefan’s Law: (area), (volume) = rate of energy radiated WAVES (speed), Speed of wave on a string: Speed of sound wave in air: (period), (F = tension, μ = m/L = mass per unit length of the string) (T in Kelvin units) 1 Doppler effect: (for mechanical waves, observer moving with vo, source moving with vs) (for EM waves, observer and source moving with relative speed, u) (I = intensity, P = sound power), Sound: Simple Harmonic Motion equation: , ELECTROMAGNETISM Coulomb’s Law: = electric force Electric fields: (point charge) (parallel plates) Electric potentials: (potential for point charge), (electric potential energy change) (potential difference across parallel plates separated by x) Circuits: , , (series) Magnetic Forces: (parallel) (point charge), Magnetic Fields: (current carrying wire) (long wire), (center of loop with N turns) (field inside solenoid with n turns/length) = magnetic flux through A Induction: = Faraday’s/Lenz’s Laws, (motional emf), (generator) Note: the directions for magnetic vector quantities are obtained using the right-hand rule. Torque on a current loop: LIGHTS AND OPTICS Snell’s Law: Thin Lens Equation: , p = object distance, q = image distance, f = focal length Magnification Equation: A DATA , circumference = , , h , G = 6.67 10 2 g = 9.80 m/s , -11 Nm2/kg2 standard atmospheric pressure = 1.013 10 Pa , (water) = 1000 kg/m3 5 σ= (Stefan-Boltzmann constant) speed of sound in air at 20 C, v = 343 m/s , o elementary charge: proton mass: , threshold of hearing, Io = 1.0 10-12 W/m2 electron mass: speed of light in a vacuum: 2